Dataset <- 
  read.csv("/Users/trekkatkins/Downloads/7585259/Rasool-Winke(2019)SystemData.csv")
summary(Dataset)
##        ID       Institution       Deg_Prog          Semester    
##  Min.   :  1   Min.   :1.000   Min.   :  1.000   Min.   :1.000  
##  1st Qu.: 58   1st Qu.:1.000   1st Qu.:  2.000   1st Qu.:1.000  
##  Median :115   Median :2.000   Median :  4.000   Median :4.000  
##  Mean   :115   Mean   :2.026   Mean   :  9.079   Mean   :3.493  
##  3rd Qu.:172   3rd Qu.:3.000   3rd Qu.:  8.000   3rd Qu.:4.000  
##  Max.   :229   Max.   :3.000   Max.   :999.000   Max.   :8.000  
##       Age             Gender       Mother_Tong       No_of_Lang    
##  Min.   : 18.00   Min.   :1.000   Min.   :  1.00   Min.   :  2.00  
##  1st Qu.: 20.00   1st Qu.:1.000   1st Qu.:  1.00   1st Qu.:  3.00  
##  Median : 21.00   Median :1.000   Median :  2.00   Median :  3.00  
##  Mean   : 42.18   Mean   :1.498   Mean   : 16.11   Mean   : 20.95  
##  3rd Qu.: 22.00   3rd Qu.:2.000   3rd Qu.:  5.00   3rd Qu.:  4.00  
##  Max.   :999.00   Max.   :2.000   Max.   :999.00   Max.   :999.00  
##  Spk_prof_Urdu     Spk_prof_Eng    Spk_prof_Pash    Spk_prof_Balo   
##  Min.   :0.0000   Min.   : 0.000   Min.   : 0.000   Min.   :0.0000  
##  1st Qu.:1.0000   1st Qu.: 1.000   1st Qu.: 0.000   1st Qu.:0.0000  
##  Median :1.0000   Median : 1.000   Median : 1.000   Median :0.0000  
##  Mean   :0.9913   Mean   : 1.109   Mean   : 0.607   Mean   :0.2489  
##  3rd Qu.:1.0000   3rd Qu.: 1.000   3rd Qu.: 1.000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :11.000   Max.   :11.000   Max.   :1.0000  
##  Spk_prof_Brah    Spk_prof_Sind    Spk_prof_Sara     Spk_prof_Pers   
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.00000   Median :0.0000  
##  Mean   :0.2009   Mean   :0.0917   Mean   :0.06114   Mean   :0.1834  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.00000   Max.   :1.0000  
##  Spk_prof_Punj    Spk_prof_Hind     Spk_prof_Other   NameOtherLang     
##  Min.   :0.0000   Min.   :0.00000   Min.   :0.0000   Length:229        
##  1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000   Class :character  
##  Median :0.0000   Median :0.00000   Median :0.0000   Mode  :character  
##  Mean   :0.1703   Mean   :0.06114   Mean   :0.0524                     
##  3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.0000                     
##  Max.   :1.0000   Max.   :1.00000   Max.   :1.0000                     
##   Lang_Aca_Ex        Sp_Slf_As        Rd_Slf_As        Wr_Slf_As     
##  Min.   :  0.000   Min.   :  1.00   Min.   :  1.00   Min.   :  1.00  
##  1st Qu.:  0.000   1st Qu.:  2.00   1st Qu.:  1.00   1st Qu.:  1.00  
##  Median :  1.000   Median :  2.00   Median :  2.00   Median :  2.00  
##  Mean   :  9.341   Mean   : 19.69   Mean   : 36.53   Mean   : 40.97  
##  3rd Qu.:  1.000   3rd Qu.:  3.00   3rd Qu.:  2.00   3rd Qu.:  2.00  
##  Max.   :999.000   Max.   :999.00   Max.   :999.00   Max.   :999.00  
##    Lis_Slf_As         Item1             Item2           Item3      
##  Min.   :  1.00   Min.   :  1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:  1.00   1st Qu.:  2.000   1st Qu.:2.000   1st Qu.:6.000  
##  Median :  2.00   Median :  5.000   Median :5.000   Median :7.000  
##  Mean   : 41.02   Mean   :  8.629   Mean   :4.197   Mean   :6.079  
##  3rd Qu.:  2.00   3rd Qu.:  6.000   3rd Qu.:6.000   3rd Qu.:7.000  
##  Max.   :999.00   Max.   :999.000   Max.   :7.000   Max.   :7.000  
##      Item4           Item5             Item6           Item7       
##  Min.   :1.000   Min.   :  1.000   Min.   :1.000   Min.   :  1.00  
##  1st Qu.:4.000   1st Qu.:  5.000   1st Qu.:2.000   1st Qu.:  5.00  
##  Median :6.000   Median :  6.000   Median :3.000   Median :  6.00  
##  Mean   :5.218   Mean   :  9.716   Mean   :3.227   Mean   :  9.79  
##  3rd Qu.:6.000   3rd Qu.:  7.000   3rd Qu.:4.000   3rd Qu.:  7.00  
##  Max.   :7.000   Max.   :999.000   Max.   :7.000   Max.   :999.00  
##      Item8             Item9           Item10          Item11     
##  Min.   :  1.000   Min.   :1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:  3.000   1st Qu.:6.000   1st Qu.:2.000   1st Qu.:2.000  
##  Median :  6.000   Median :6.000   Median :4.000   Median :5.000  
##  Mean   :  9.179   Mean   :6.118   Mean   :4.035   Mean   :4.131  
##  3rd Qu.:  6.000   3rd Qu.:7.000   3rd Qu.:6.000   3rd Qu.:6.000  
##  Max.   :999.000   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##      Item12          Item13          Item14         Item15     
##  Min.   :1.000   Min.   :1.000   Min.   :1.00   Min.   :1.000  
##  1st Qu.:2.000   1st Qu.:4.000   1st Qu.:2.00   1st Qu.:4.000  
##  Median :5.000   Median :6.000   Median :5.00   Median :6.000  
##  Mean   :4.415   Mean   :5.183   Mean   :4.21   Mean   :5.271  
##  3rd Qu.:6.000   3rd Qu.:7.000   3rd Qu.:6.00   3rd Qu.:7.000  
##  Max.   :7.000   Max.   :7.000   Max.   :7.00   Max.   :7.000  
##      Item16           Item17            Item18          Item19      
##  Min.   :  1.00   Min.   :  1.000   Min.   :1.000   Min.   :  1.00  
##  1st Qu.:  5.00   1st Qu.:  3.000   1st Qu.:4.000   1st Qu.:  5.00  
##  Median :  6.00   Median :  5.000   Median :6.000   Median :  6.00  
##  Mean   : 22.79   Mean   :  9.013   Mean   :5.314   Mean   : 14.24  
##  3rd Qu.:  7.00   3rd Qu.:  6.000   3rd Qu.:7.000   3rd Qu.:  7.00  
##  Max.   :999.00   Max.   :999.000   Max.   :7.000   Max.   :999.00  
##      Item20           Item21          Item22          Item23     
##  Min.   :  1.00   Min.   :1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:  5.00   1st Qu.:4.000   1st Qu.:5.000   1st Qu.:6.000  
##  Median :  6.00   Median :6.000   Median :6.000   Median :7.000  
##  Mean   : 13.99   Mean   :5.262   Mean   :5.712   Mean   :6.262  
##  3rd Qu.:  7.00   3rd Qu.:7.000   3rd Qu.:7.000   3rd Qu.:7.000  
##  Max.   :999.00   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##      Item24          Item25           Item26            Item27     
##  Min.   :1.000   Min.   :  1.00   Min.   :  1.000   Min.   :1.000  
##  1st Qu.:4.000   1st Qu.:  6.00   1st Qu.:  2.000   1st Qu.:2.000  
##  Median :6.000   Median :  6.00   Median :  5.000   Median :3.000  
##  Mean   :5.201   Mean   : 10.33   Mean   :  8.699   Mean   :3.642  
##  3rd Qu.:6.000   3rd Qu.:  7.00   3rd Qu.:  6.000   3rd Qu.:6.000  
##  Max.   :7.000   Max.   :999.00   Max.   :999.000   Max.   :7.000  
##      Item28          Item29          Item30            Item31     
##  Min.   :1.000   Min.   :1.000   Min.   :  1.000   Min.   :1.000  
##  1st Qu.:5.000   1st Qu.:5.000   1st Qu.:  4.000   1st Qu.:6.000  
##  Median :6.000   Median :6.000   Median :  6.000   Median :6.000  
##  Mean   :5.681   Mean   :5.563   Mean   :  9.345   Mean   :5.996  
##  3rd Qu.:7.000   3rd Qu.:7.000   3rd Qu.:  7.000   3rd Qu.:7.000  
##  Max.   :7.000   Max.   :7.000   Max.   :999.000   Max.   :7.000  
##      Item32           Item33           Item34           Item35     
##  Min.   :  1.00   Min.   :  1.00   Min.   :  1.00   Min.   :1.000  
##  1st Qu.:  5.00   1st Qu.:  6.00   1st Qu.:  3.00   1st Qu.:6.000  
##  Median :  6.00   Median :  6.00   Median :  5.00   Median :6.000  
##  Mean   : 14.53   Mean   : 10.35   Mean   : 13.28   Mean   :5.926  
##  3rd Qu.:  7.00   3rd Qu.:  7.00   3rd Qu.:  6.00   3rd Qu.:7.000  
##  Max.   :999.00   Max.   :999.00   Max.   :999.00   Max.   :7.000  
##      item36           Item37          Item38           Item39     
##  Min.   :  1.00   Min.   :1.000   Min.   :  1.00   Min.   :1.000  
##  1st Qu.:  2.00   1st Qu.:5.000   1st Qu.:  3.00   1st Qu.:2.000  
##  Median :  4.00   Median :6.000   Median :  5.00   Median :5.000  
##  Mean   : 12.48   Mean   :5.716   Mean   : 13.38   Mean   :4.624  
##  3rd Qu.:  6.00   3rd Qu.:7.000   3rd Qu.:  6.00   3rd Qu.:7.000  
##  Max.   :999.00   Max.   :7.000   Max.   :999.00   Max.   :7.000  
##      Item40            Item41           Item42           Item43      
##  Min.   :  1.000   Min.   :  1.00   Min.   :  1.00   Min.   :  1.00  
##  1st Qu.:  1.000   1st Qu.:  5.00   1st Qu.:  4.00   1st Qu.:  6.00  
##  Median :  2.000   Median :  6.00   Median :  6.00   Median :  6.00  
##  Mean   :  7.384   Mean   : 14.29   Mean   : 22.45   Mean   : 32.04  
##  3rd Qu.:  5.000   3rd Qu.:  7.00   3rd Qu.:  7.00   3rd Qu.:  7.00  
##  Max.   :999.000   Max.   :999.00   Max.   :999.00   Max.   :999.00  
##      Item44           Item45          Item46           Item47     
##  Min.   :  1.00   Min.   :1.000   Min.   :  1.00   Min.   :1.000  
##  1st Qu.:  5.00   1st Qu.:4.000   1st Qu.:  5.00   1st Qu.:4.000  
##  Median :  6.00   Median :6.000   Median :  6.00   Median :5.000  
##  Mean   : 14.05   Mean   :5.262   Mean   : 14.13   Mean   :4.987  
##  3rd Qu.:  7.00   3rd Qu.:6.000   3rd Qu.:  7.00   3rd Qu.:6.000  
##  Max.   :999.00   Max.   :7.000   Max.   :999.00   Max.   :9.000  
##      Item48           Item49            Item50          Item51     
##  Min.   :  1.00   Min.   :  1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:  6.00   1st Qu.:  4.000   1st Qu.:3.000   1st Qu.:4.000  
##  Median :  6.00   Median :  5.000   Median :5.000   Median :6.000  
##  Mean   : 14.67   Mean   :  9.227   Mean   :4.428   Mean   :5.367  
##  3rd Qu.:  7.00   3rd Qu.:  6.000   3rd Qu.:6.000   3rd Qu.:7.000  
##  Max.   :999.00   Max.   :999.000   Max.   :7.000   Max.   :7.000  
##      Item52           Item53          Item54     
##  Min.   :  1.00   Min.   :1.000   Min.   :1.000  
##  1st Qu.:  6.00   1st Qu.:6.000   1st Qu.:4.000  
##  Median :  6.00   Median :7.000   Median :5.000  
##  Mean   : 18.92   Mean   :6.192   Mean   :4.699  
##  3rd Qu.:  7.00   3rd Qu.:7.000   3rd Qu.:6.000  
##  Max.   :999.00   Max.   :7.000   Max.   :7.000
#sampling
set.seed(12)
sample <- Dataset[sample(1:nrow(Dataset), 36,
   replace=FALSE),]
sample$Gender <- as.factor(sample$Gender)
str(sample)
## 'data.frame':    36 obs. of  79 variables:
##  $ ID            : int  194 90 80 91 174 197 69 220 34 136 ...
##  $ Institution   : int  1 2 2 2 1 1 3 1 3 2 ...
##  $ Deg_Prog      : int  2 3 3 3 1 1 10 1 5 4 ...
##  $ Semester      : int  4 4 4 4 1 4 7 1 5 4 ...
##  $ Age           : int  23 22 20 23 21 24 22 20 20 22 ...
##  $ Gender        : Factor w/ 2 levels "1","2": 1 1 1 1 1 2 2 1 2 1 ...
##  $ Mother_Tong   : int  1 2 2 1 1 1 1 2 6 1 ...
##  $ No_of_Lang    : int  6 3 5 3 3 3 3 4 3 3 ...
##  $ Spk_prof_Urdu : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Spk_prof_Eng  : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Spk_prof_Pash : int  1 0 0 1 1 1 1 0 0 1 ...
##  $ Spk_prof_Balo : int  1 1 1 0 0 0 0 1 0 0 ...
##  $ Spk_prof_Brah : int  1 0 1 0 0 0 0 0 0 0 ...
##  $ Spk_prof_Sind : int  0 0 1 0 0 0 0 1 0 0 ...
##  $ Spk_prof_Sara : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Spk_prof_Pers : int  1 0 0 0 0 0 0 0 1 0 ...
##  $ Spk_prof_Punj : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Spk_prof_Hind : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Spk_prof_Other: int  0 0 0 0 0 0 0 0 0 0 ...
##  $ NameOtherLang : chr  " " " " " " " " ...
##  $ Lang_Aca_Ex   : int  0 1 1 0 1 0 1 1 1 1 ...
##  $ Sp_Slf_As     : int  2 2 2 3 3 1 2 1 1 1 ...
##  $ Rd_Slf_As     : int  1 2 2 2 2 1 1 2 2 1 ...
##  $ Wr_Slf_As     : int  2 2 3 2 2 1 2 1 2 2 ...
##  $ Lis_Slf_As    : int  2 2 3 3 1 2 2 2 2 2 ...
##  $ Item1         : int  2 4 6 1 1 3 2 6 5 1 ...
##  $ Item2         : int  5 7 7 6 2 1 4 1 7 6 ...
##  $ Item3         : int  7 6 7 7 7 3 7 5 7 6 ...
##  $ Item4         : int  5 6 4 5 5 7 6 6 7 7 ...
##  $ Item5         : int  5 7 6 7 7 6 2 5 6 1 ...
##  $ Item6         : int  3 5 3 4 7 3 6 2 2 1 ...
##  $ Item7         : int  6 7 6 6 4 6 7 7 7 5 ...
##  $ Item8         : int  6 6 5 6 6 6 7 7 7 5 ...
##  $ Item9         : int  5 7 7 7 6 7 7 6 7 7 ...
##  $ Item10        : int  2 7 7 3 7 7 7 2 4 6 ...
##  $ Item11        : int  4 1 1 7 5 1 6 6 2 3 ...
##  $ Item12        : int  2 6 1 6 3 5 6 2 6 5 ...
##  $ Item13        : int  6 7 4 5 6 4 7 6 7 6 ...
##  $ Item14        : int  5 5 7 7 3 7 7 2 5 6 ...
##  $ Item15        : int  6 1 2 2 7 7 3 2 6 7 ...
##  $ Item16        : int  3 7 7 5 6 7 7 6 7 5 ...
##  $ Item17        : int  1 2 2 3 5 7 7 6 6 6 ...
##  $ Item18        : int  1 7 7 6 7 1 6 2 7 7 ...
##  $ Item19        : int  5 6 4 5 2 7 6 7 6 5 ...
##  $ Item20        : int  6 3 2 1 5 7 6 6 6 6 ...
##  $ Item21        : int  4 6 2 1 7 7 7 5 6 7 ...
##  $ Item22        : int  2 7 6 4 6 4 6 2 7 7 ...
##  $ Item23        : int  6 5 7 6 7 7 7 6 7 7 ...
##  $ Item24        : int  3 4 2 2 1 7 5 6 7 6 ...
##  $ Item25        : int  6 4 4 6 6 7 6 6 6 5 ...
##  $ Item26        : int  2 2 1 5 4 2 6 6 4 2 ...
##  $ Item27        : int  2 5 6 1 1 5 2 2 5 3 ...
##  $ Item28        : int  2 6 1 6 7 7 6 2 5 7 ...
##  $ Item29        : int  2 6 7 5 7 7 7 6 6 5 ...
##  $ Item30        : int  1 6 7 5 5 4 7 6 6 6 ...
##  $ Item31        : int  5 7 5 5 7 7 7 6 7 7 ...
##  $ Item32        : int  6 6 6 3 7 7 6 2 7 7 ...
##  $ Item33        : int  6 7 2 6 7 7 4 6 7 7 ...
##  $ Item34        : int  3 3 4 6 6 6 7 6 2 7 ...
##  $ Item35        : int  6 7 7 6 6 7 6 6 6 7 ...
##  $ item36        : int  7 1 5 3 1 5 5 7 4 5 ...
##  $ Item37        : int  2 6 6 4 7 7 6 7 6 7 ...
##  $ Item38        : int  2 2 2 4 4 2 6 6 3 3 ...
##  $ Item39        : int  2 3 6 4 7 6 7 7 3 1 ...
##  $ Item40        : int  4 4 2 1 1 1 1 2 2 3 ...
##  $ Item41        : int  5 7 5 6 7 6 6 7 6 7 ...
##  $ Item42        : int  3 6 2 1 7 7 6 2 5 7 ...
##  $ Item43        : int  3 5 6 3 6 7 7 6 6 7 ...
##  $ Item44        : int  3 4 5 4 4 7 7 6 6 7 ...
##  $ Item45        : int  6 6 3 4 5 7 7 6 5 5 ...
##  $ Item46        : int  6 6 6 4 4 4 6 5 6 6 ...
##  $ Item47        : int  6 6 6 5 7 1 6 2 6 6 ...
##  $ Item48        : int  6 6 6 4 1 7 6 6 7 6 ...
##  $ Item49        : int  7 1 4 1 5 4 5 7 6 7 ...
##  $ Item50        : int  6 6 1 4 5 1 6 6 3 4 ...
##  $ Item51        : int  6 6 7 6 7 3 7 2 6 7 ...
##  $ Item52        : int  6 7 7 6 6 7 7 7 5 7 ...
##  $ Item53        : int  6 7 6 6 5 7 6 7 7 7 ...
##  $ Item54        : int  2 7 2 4 6 5 5 5 6 5 ...
set.seed(34)
sample2 <- Dataset[sample(1:nrow(Dataset), 36,
   replace=FALSE),]
sample2$Gender <- as.factor(sample$Gender)
str(sample2)
## 'data.frame':    36 obs. of  79 variables:
##  $ ID            : int  221 161 137 10 50 8 86 182 100 29 ...
##  $ Institution   : int  1 1 2 3 3 3 2 1 2 3 ...
##  $ Deg_Prog      : int  2 1 4 6 9 7 3 1 3 5 ...
##  $ Semester      : int  1 1 2 5 5 1 4 1 4 1 ...
##  $ Age           : int  19 22 19 22 20 19 21 23 20 18 ...
##  $ Gender        : Factor w/ 2 levels "1","2": 1 1 1 1 1 2 2 1 2 1 ...
##  $ Mother_Tong   : int  5 4 2 6 11 6 5 2 1 3 ...
##  $ No_of_Lang    : int  3 5 3 3 4 3 3 10 4 4 ...
##  $ Spk_prof_Urdu : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Spk_prof_Eng  : int  1 1 1 1 1 1 1 1 11 1 ...
##  $ Spk_prof_Pash : int  0 1 0 0 0 0 0 1 1 0 ...
##  $ Spk_prof_Balo : int  0 0 1 0 0 0 0 1 0 1 ...
##  $ Spk_prof_Brah : int  0 0 0 0 1 0 0 1 0 1 ...
##  $ Spk_prof_Sind : int  0 0 0 0 1 0 0 1 0 0 ...
##  $ Spk_prof_Sara : int  0 0 0 0 0 0 0 1 1 0 ...
##  $ Spk_prof_Pers : int  0 0 0 1 0 1 0 1 0 0 ...
##  $ Spk_prof_Punj : int  1 1 0 0 0 0 1 1 0 0 ...
##  $ Spk_prof_Hind : int  0 1 0 0 0 0 0 1 0 0 ...
##  $ Spk_prof_Other: int  0 0 0 0 0 0 0 0 0 0 ...
##  $ NameOtherLang : chr  " " " " " " " " ...
##  $ Lang_Aca_Ex   : int  1 1 1 1 0 1 1 0 0 1 ...
##  $ Sp_Slf_As     : int  1 2 2 2 999 1 3 2 3 2 ...
##  $ Rd_Slf_As     : int  2 3 2 1 999 1 3 999 2 1 ...
##  $ Wr_Slf_As     : int  2 2 2 2 999 2 3 999 3 1 ...
##  $ Lis_Slf_As    : int  1 2 2 2 999 1 2 999 3 1 ...
##  $ Item1         : int  7 1 7 5 6 1 1 1 6 6 ...
##  $ Item2         : int  7 2 6 4 2 6 4 3 2 2 ...
##  $ Item3         : int  7 7 7 7 1 7 6 7 6 7 ...
##  $ Item4         : int  6 2 6 6 1 6 6 1 2 4 ...
##  $ Item5         : int  7 4 6 7 6 6 6 4 2 6 ...
##  $ Item6         : int  1 3 3 2 2 4 6 5 2 6 ...
##  $ Item7         : int  6 6 6 7 1 6 1 1 6 6 ...
##  $ Item8         : int  5 5 5 7 6 4 2 7 2 6 ...
##  $ Item9         : int  6 7 6 7 6 6 4 7 6 7 ...
##  $ Item10        : int  2 5 3 1 1 6 4 7 2 4 ...
##  $ Item11        : int  7 5 7 3 2 1 3 1 6 6 ...
##  $ Item12        : int  1 4 5 4 6 4 1 1 6 6 ...
##  $ Item13        : int  2 6 7 7 6 6 2 7 2 5 ...
##  $ Item14        : int  7 5 1 1 2 6 4 5 2 6 ...
##  $ Item15        : int  7 2 7 7 1 6 5 1 6 6 ...
##  $ Item16        : int  6 6 6 7 1 6 2 5 2 6 ...
##  $ Item17        : int  6 6 5 4 1 4 2 7 2 7 ...
##  $ Item18        : int  6 6 7 4 2 4 4 7 2 6 ...
##  $ Item19        : int  7 6 7 7 6 4 4 1 6 7 ...
##  $ Item20        : int  7 7 7 7 2 6 5 1 2 7 ...
##  $ Item21        : int  1 5 6 7 2 7 5 7 2 6 ...
##  $ Item22        : int  6 4 5 7 6 6 3 6 2 6 ...
##  $ Item23        : int  6 7 7 7 6 6 6 6 6 7 ...
##  $ Item24        : int  5 4 2 7 6 6 6 5 6 6 ...
##  $ Item25        : int  7 6 7 7 2 6 4 7 6 7 ...
##  $ Item26        : int  6 6 6 7 3 2 6 4 6 7 ...
##  $ Item27        : int  2 6 1 1 2 2 2 7 2 4 ...
##  $ Item28        : int  7 7 7 7 4 6 2 6 6 7 ...
##  $ Item29        : int  7 7 6 7 2 6 3 1 2 7 ...
##  $ Item30        : int  1 6 7 7 2 6 4 7 999 6 ...
##  $ Item31        : int  6 6 7 7 6 7 5 6 2 7 ...
##  $ Item32        : int  6 6 6 4 6 6 5 6 999 7 ...
##  $ Item33        : int  7 7 5 7 6 6 6 4 6 7 ...
##  $ Item34        : int  6 4 7 5 2 1 4 1 999 4 ...
##  $ Item35        : int  6 5 6 7 5 7 2 1 6 6 ...
##  $ item36        : int  7 7 2 1 4 4 2 1 999 2 ...
##  $ Item37        : int  7 7 6 7 2 4 6 1 2 6 ...
##  $ Item38        : int  6 5 5 6 6 2 6 1 999 6 ...
##  $ Item39        : int  1 4 4 7 1 7 4 1 2 6 ...
##  $ Item40        : int  2 1 3 7 3 2 2 4 999 1 ...
##  $ Item41        : int  1 7 7 7 7 6 6 7 6 6 ...
##  $ Item42        : int  7 7 6 7 6 6 5 1 999 7 ...
##  $ Item43        : int  7 7 6 7 3 6 4 6 6 7 ...
##  $ Item44        : int  7 4 6 7 4 6 2 1 999 6 ...
##  $ Item45        : int  6 4 4 7 3 6 6 7 6 6 ...
##  $ Item46        : int  7 5 4 7 3 6 2 1 999 6 ...
##  $ Item47        : int  7 3 6 7 6 6 4 7 2 4 ...
##  $ Item48        : int  7 6 7 7 6 7 6 7 6 7 ...
##  $ Item49        : int  6 4 6 7 2 6 4 1 6 6 ...
##  $ Item50        : int  6 5 6 5 3 1 6 1 2 6 ...
##  $ Item51        : int  2 6 6 7 4 7 4 7 6 6 ...
##  $ Item52        : int  7 7 5 7 999 6 6 4 6 6 ...
##  $ Item53        : int  6 7 6 7 6 6 6 7 6 7 ...
##  $ Item54        : int  6 5 7 4 6 6 4 1 6 2 ...
summary(sample)
##        ID         Institution       Deg_Prog         Semester   
##  Min.   : 13.0   Min.   :1.000   Min.   : 1.000   Min.   :1.00  
##  1st Qu.: 81.5   1st Qu.:1.000   1st Qu.: 2.000   1st Qu.:1.00  
##  Median :126.0   Median :2.000   Median : 3.000   Median :4.00  
##  Mean   :132.4   Mean   :1.806   Mean   : 4.556   Mean   :3.75  
##  3rd Qu.:186.5   3rd Qu.:2.000   3rd Qu.: 5.250   3rd Qu.:4.25  
##  Max.   :226.0   Max.   :3.000   Max.   :13.000   Max.   :8.00  
##       Age        Gender  Mother_Tong      No_of_Lang    Spk_prof_Urdu
##  Min.   :18.00   1:21   Min.   :1.000   Min.   :2.000   Min.   :1    
##  1st Qu.:20.00   2:15   1st Qu.:1.000   1st Qu.:3.000   1st Qu.:1    
##  Median :21.00          Median :1.000   Median :3.000   Median :1    
##  Mean   :21.08          Mean   :1.861   Mean   :3.639   Mean   :1    
##  3rd Qu.:22.00          3rd Qu.:2.000   3rd Qu.:4.000   3rd Qu.:1    
##  Max.   :24.00          Max.   :6.000   Max.   :8.000   Max.   :1    
##   Spk_prof_Eng    Spk_prof_Pash    Spk_prof_Balo    Spk_prof_Brah   
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:1.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :1.0000   Median :1.0000   Median :0.0000   Median :0.0000  
##  Mean   :0.9722   Mean   :0.6111   Mean   :0.2778   Mean   :0.1667  
##  3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##  Spk_prof_Sind    Spk_prof_Sara     Spk_prof_Pers    Spk_prof_Punj   
##  Min.   :0.0000   Min.   :0.00000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.00000   Median :0.0000   Median :0.0000  
##  Mean   :0.1111   Mean   :0.02778   Mean   :0.2222   Mean   :0.1667  
##  3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.00000   Max.   :1.0000   Max.   :1.0000  
##  Spk_prof_Hind     Spk_prof_Other    NameOtherLang       Lang_Aca_Ex    
##  Min.   :0.00000   Min.   :0.00000   Length:36          Min.   :0.0000  
##  1st Qu.:0.00000   1st Qu.:0.00000   Class :character   1st Qu.:0.0000  
##  Median :0.00000   Median :0.00000   Mode  :character   Median :1.0000  
##  Mean   :0.02778   Mean   :0.05556                      Mean   :0.6111  
##  3rd Qu.:0.00000   3rd Qu.:0.00000                      3rd Qu.:1.0000  
##  Max.   :1.00000   Max.   :1.00000                      Max.   :1.0000  
##    Sp_Slf_As        Rd_Slf_As        Wr_Slf_As        Lis_Slf_As    
##  Min.   :  1.00   Min.   :  1.00   Min.   :  1.00   Min.   :  1.00  
##  1st Qu.:  2.00   1st Qu.:  1.00   1st Qu.:  2.00   1st Qu.:  2.00  
##  Median :  2.00   Median :  2.00   Median :  2.00   Median :  2.00  
##  Mean   : 57.42   Mean   : 84.75   Mean   : 84.94   Mean   : 85.11  
##  3rd Qu.:  3.00   3rd Qu.:  2.00   3rd Qu.:  2.00   3rd Qu.:  2.00  
##  Max.   :999.00   Max.   :999.00   Max.   :999.00   Max.   :999.00  
##      Item1           Item2          Item3           Item4           Item5      
##  Min.   :1.000   Min.   :1.00   Min.   :3.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:2.000   1st Qu.:2.00   1st Qu.:7.000   1st Qu.:5.000   1st Qu.:5.000  
##  Median :6.000   Median :6.00   Median :7.000   Median :6.000   Median :6.000  
##  Mean   :4.722   Mean   :4.50   Mean   :6.639   Mean   :5.583   Mean   :5.583  
##  3rd Qu.:7.000   3rd Qu.:6.25   3rd Qu.:7.000   3rd Qu.:7.000   3rd Qu.:7.000  
##  Max.   :7.000   Max.   :7.00   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##      Item6           Item7           Item8           Item9         Item10     
##  Min.   :1.000   Min.   :2.000   Min.   :1.000   Min.   :4.0   Min.   :1.000  
##  1st Qu.:2.000   1st Qu.:5.000   1st Qu.:4.000   1st Qu.:6.0   1st Qu.:1.000  
##  Median :3.000   Median :6.000   Median :6.000   Median :7.0   Median :3.000  
##  Mean   :3.333   Mean   :5.861   Mean   :5.194   Mean   :6.5   Mean   :3.778  
##  3rd Qu.:4.000   3rd Qu.:7.000   3rd Qu.:7.000   3rd Qu.:7.0   3rd Qu.:6.000  
##  Max.   :7.000   Max.   :7.000   Max.   :7.000   Max.   :7.0   Max.   :7.000  
##      Item11      Item12         Item13          Item14          Item15    
##  Min.   :1   Min.   :1.00   Min.   :1.000   Min.   :1.000   Min.   :1.00  
##  1st Qu.:2   1st Qu.:3.00   1st Qu.:4.000   1st Qu.:2.750   1st Qu.:4.75  
##  Median :4   Median :6.00   Median :6.000   Median :5.500   Median :6.00  
##  Mean   :4   Mean   :4.75   Mean   :5.417   Mean   :4.611   Mean   :5.50  
##  3rd Qu.:6   3rd Qu.:6.00   3rd Qu.:7.000   3rd Qu.:6.000   3rd Qu.:7.00  
##  Max.   :7   Max.   :7.00   Max.   :7.000   Max.   :7.000   Max.   :7.00  
##      Item16          Item17          Item18          Item19     
##  Min.   :3.000   Min.   :1.000   Min.   :1.000   Min.   :2.000  
##  1st Qu.:5.750   1st Qu.:2.750   1st Qu.:6.000   1st Qu.:5.000  
##  Median :6.000   Median :6.000   Median :6.500   Median :6.000  
##  Mean   :6.028   Mean   :4.806   Mean   :5.972   Mean   :5.778  
##  3rd Qu.:7.000   3rd Qu.:6.250   3rd Qu.:7.000   3rd Qu.:7.000  
##  Max.   :7.000   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##      Item20          Item21      Item22          Item23          Item24     
##  Min.   :1.000   Min.   :1   Min.   :1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:5.000   1st Qu.:4   1st Qu.:5.000   1st Qu.:6.000   1st Qu.:4.000  
##  Median :6.000   Median :6   Median :6.000   Median :7.000   Median :6.000  
##  Mean   :5.611   Mean   :5   Mean   :5.528   Mean   :6.333   Mean   :5.167  
##  3rd Qu.:7.000   3rd Qu.:6   3rd Qu.:7.000   3rd Qu.:7.000   3rd Qu.:7.000  
##  Max.   :7.000   Max.   :7   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##      Item25          Item26          Item27          Item28     
##  Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:6.000   1st Qu.:2.000   1st Qu.:2.000   1st Qu.:5.000  
##  Median :6.500   Median :5.000   Median :3.000   Median :6.000  
##  Mean   :6.139   Mean   :4.111   Mean   :3.528   Mean   :5.556  
##  3rd Qu.:7.000   3rd Qu.:6.000   3rd Qu.:6.000   3rd Qu.:7.000  
##  Max.   :7.000   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##      Item29          Item30          Item31          Item32     
##  Min.   :2.000   Min.   :1.000   Min.   :5.000   Min.   :2.000  
##  1st Qu.:6.000   1st Qu.:5.000   1st Qu.:6.000   1st Qu.:6.000  
##  Median :6.000   Median :6.000   Median :7.000   Median :7.000  
##  Mean   :6.222   Mean   :5.194   Mean   :6.444   Mean   :6.167  
##  3rd Qu.:7.000   3rd Qu.:7.000   3rd Qu.:7.000   3rd Qu.:7.000  
##  Max.   :7.000   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##      Item33          Item34          Item35          item36     
##  Min.   :2.000   Min.   :1.000   Min.   :2.000   Min.   :1.000  
##  1st Qu.:6.000   1st Qu.:4.000   1st Qu.:6.000   1st Qu.:2.000  
##  Median :6.500   Median :6.000   Median :6.000   Median :4.500  
##  Mean   :6.139   Mean   :4.917   Mean   :6.167   Mean   :4.111  
##  3rd Qu.:7.000   3rd Qu.:6.000   3rd Qu.:7.000   3rd Qu.:6.000  
##  Max.   :7.000   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##      Item37          Item38      Item39          Item40          Item41     
##  Min.   :1.000   Min.   :1   Min.   :1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:6.000   1st Qu.:2   1st Qu.:2.750   1st Qu.:1.000   1st Qu.:5.000  
##  Median :6.500   Median :4   Median :5.000   Median :2.000   Median :6.000  
##  Mean   :5.917   Mean   :4   Mean   :4.528   Mean   :3.111   Mean   :5.694  
##  3rd Qu.:7.000   3rd Qu.:6   3rd Qu.:7.000   3rd Qu.:5.250   3rd Qu.:7.000  
##  Max.   :7.000   Max.   :7   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##      Item42        Item43      Item44          Item45          Item46     
##  Min.   :1.0   Min.   :3   Min.   :1.000   Min.   :1.000   Min.   :2.000  
##  1st Qu.:5.0   1st Qu.:6   1st Qu.:4.750   1st Qu.:5.000   1st Qu.:5.000  
##  Median :6.0   Median :6   Median :6.000   Median :6.000   Median :6.000  
##  Mean   :5.5   Mean   :6   Mean   :5.389   Mean   :5.417   Mean   :5.611  
##  3rd Qu.:7.0   3rd Qu.:7   3rd Qu.:7.000   3rd Qu.:6.000   3rd Qu.:6.000  
##  Max.   :7.0   Max.   :7   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##      Item47          Item48          Item49          Item50     
##  Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:4.000   1st Qu.:6.000   1st Qu.:4.000   1st Qu.:2.000  
##  Median :6.000   Median :6.000   Median :6.000   Median :5.000  
##  Mean   :5.111   Mean   :6.222   Mean   :5.028   Mean   :4.278  
##  3rd Qu.:6.250   3rd Qu.:7.000   3rd Qu.:6.000   3rd Qu.:6.000  
##  Max.   :7.000   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##      Item51          Item52          Item53          Item54     
##  Min.   :1.000   Min.   :4.000   Min.   :2.000   Min.   :1.000  
##  1st Qu.:5.750   1st Qu.:6.000   1st Qu.:6.000   1st Qu.:3.750  
##  Median :6.000   Median :7.000   Median :6.000   Median :5.000  
##  Mean   :5.583   Mean   :6.389   Mean   :6.278   Mean   :4.667  
##  3rd Qu.:7.000   3rd Qu.:7.000   3rd Qu.:7.000   3rd Qu.:6.000  
##  Max.   :7.000   Max.   :7.000   Max.   :7.000   Max.   :7.000
summary(sample2)
##        ID         Institution       Deg_Prog         Semester    
##  Min.   :  8.0   Min.   :1.000   Min.   : 1.000   Min.   :1.000  
##  1st Qu.: 43.5   1st Qu.:1.000   1st Qu.: 2.000   1st Qu.:1.000  
##  Median : 99.5   Median :2.000   Median : 3.500   Median :4.000  
##  Mean   :110.1   Mean   :2.028   Mean   : 4.056   Mean   :3.056  
##  3rd Qu.:172.2   3rd Qu.:3.000   3rd Qu.: 5.250   3rd Qu.:4.000  
##  Max.   :222.0   Max.   :3.000   Max.   :10.000   Max.   :7.000  
##       Age         Gender  Mother_Tong       No_of_Lang     Spk_prof_Urdu
##  Min.   : 18.00   1:21   Min.   : 1.000   Min.   : 2.000   Min.   :1    
##  1st Qu.: 19.75   2:15   1st Qu.: 2.000   1st Qu.: 3.000   1st Qu.:1    
##  Median : 20.00          Median : 4.000   Median : 3.000   Median :1    
##  Mean   : 47.86          Mean   : 4.167   Mean   : 3.444   Mean   :1    
##  3rd Qu.: 22.00          3rd Qu.: 6.000   3rd Qu.: 4.000   3rd Qu.:1    
##  Max.   :999.00          Max.   :11.000   Max.   :10.000   Max.   :1    
##   Spk_prof_Eng   Spk_prof_Pash    Spk_prof_Balo    Spk_prof_Brah   
##  Min.   : 0.00   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.: 1.00   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median : 1.00   Median :0.0000   Median :0.0000   Median :0.0000  
##  Mean   : 1.25   Mean   :0.3056   Mean   :0.1944   Mean   :0.1944  
##  3rd Qu.: 1.00   3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:0.0000  
##  Max.   :11.00   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##  Spk_prof_Sind    Spk_prof_Sara     Spk_prof_Pers  Spk_prof_Punj   
##  Min.   :0.0000   Min.   :0.00000   Min.   :0.00   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.00   1st Qu.:0.0000  
##  Median :0.0000   Median :0.00000   Median :0.00   Median :0.0000  
##  Mean   :0.1111   Mean   :0.08333   Mean   :0.25   Mean   :0.2222  
##  3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.25   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.00000   Max.   :1.00   Max.   :1.0000  
##  Spk_prof_Hind    Spk_prof_Other    NameOtherLang       Lang_Aca_Ex    
##  Min.   :0.0000   Min.   :0.00000   Length:36          Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.00000   Class :character   1st Qu.:0.0000  
##  Median :0.0000   Median :0.00000   Mode  :character   Median :1.0000  
##  Mean   :0.1111   Mean   :0.02778                      Mean   :0.7222  
##  3rd Qu.:0.0000   3rd Qu.:0.00000                      3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :1.00000                      Max.   :1.0000  
##    Sp_Slf_As        Rd_Slf_As        Wr_Slf_As        Lis_Slf_As    
##  Min.   :  1.00   Min.   :  1.00   Min.   :  1.00   Min.   :  1.00  
##  1st Qu.:  2.00   1st Qu.:  1.00   1st Qu.:  1.00   1st Qu.:  1.00  
##  Median :  2.00   Median :  2.00   Median :  2.00   Median :  2.00  
##  Mean   : 29.72   Mean   : 57.36   Mean   : 57.25   Mean   : 57.25  
##  3rd Qu.:  2.25   3rd Qu.:  2.00   3rd Qu.:  2.00   3rd Qu.:  2.00  
##  Max.   :999.00   Max.   :999.00   Max.   :999.00   Max.   :999.00  
##      Item1           Item2           Item3           Item4          Item5      
##  Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.00   Min.   :1.000  
##  1st Qu.:1.000   1st Qu.:2.000   1st Qu.:6.000   1st Qu.:4.75   1st Qu.:5.000  
##  Median :5.000   Median :4.000   Median :7.000   Median :6.00   Median :6.000  
##  Mean   :3.917   Mean   :4.028   Mean   :6.111   Mean   :5.25   Mean   :5.556  
##  3rd Qu.:6.000   3rd Qu.:6.000   3rd Qu.:7.000   3rd Qu.:6.00   3rd Qu.:7.000  
##  Max.   :7.000   Max.   :7.000   Max.   :7.000   Max.   :7.00   Max.   :7.000  
##      Item6           Item7           Item8           Item9      
##  Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:2.000   1st Qu.:5.000   1st Qu.:4.000   1st Qu.:6.000  
##  Median :3.000   Median :6.000   Median :6.000   Median :6.000  
##  Mean   :3.389   Mean   :5.333   Mean   :4.972   Mean   :6.083  
##  3rd Qu.:4.250   3rd Qu.:6.000   3rd Qu.:6.000   3rd Qu.:7.000  
##  Max.   :7.000   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##      Item10          Item11          Item12      Item13          Item14     
##  Min.   :1.000   Min.   :1.000   Min.   :1   Min.   :1.000   Min.   :1.000  
##  1st Qu.:2.000   1st Qu.:1.750   1st Qu.:2   1st Qu.:4.000   1st Qu.:2.000  
##  Median :4.000   Median :4.000   Median :4   Median :6.000   Median :6.000  
##  Mean   :4.111   Mean   :3.833   Mean   :4   Mean   :5.194   Mean   :4.667  
##  3rd Qu.:6.000   3rd Qu.:6.000   3rd Qu.:6   3rd Qu.:7.000   3rd Qu.:7.000  
##  Max.   :7.000   Max.   :7.000   Max.   :7   Max.   :7.000   Max.   :7.000  
##      Item15          Item16           Item17          Item18     
##  Min.   :1.000   Min.   :  1.00   Min.   :1.000   Min.   :1.000  
##  1st Qu.:4.750   1st Qu.:  6.00   1st Qu.:3.000   1st Qu.:4.000  
##  Median :6.000   Median :  6.00   Median :5.000   Median :6.000  
##  Mean   :5.278   Mean   : 33.36   Mean   :4.722   Mean   :5.167  
##  3rd Qu.:7.000   3rd Qu.:  7.00   3rd Qu.:6.000   3rd Qu.:7.000  
##  Max.   :7.000   Max.   :999.00   Max.   :7.000   Max.   :7.000  
##      Item19         Item20          Item21          Item22          Item23     
##  Min.   :1.00   Min.   :1.000   Min.   :1.000   Min.   :2.000   Min.   :5.000  
##  1st Qu.:5.00   1st Qu.:4.000   1st Qu.:4.750   1st Qu.:5.000   1st Qu.:6.000  
##  Median :6.00   Median :6.000   Median :6.000   Median :6.000   Median :6.500  
##  Mean   :5.75   Mean   :5.306   Mean   :5.278   Mean   :5.472   Mean   :6.444  
##  3rd Qu.:7.00   3rd Qu.:7.000   3rd Qu.:7.000   3rd Qu.:7.000   3rd Qu.:7.000  
##  Max.   :7.00   Max.   :7.000   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##      Item24          Item25          Item26           Item27     
##  Min.   :1.000   Min.   :2.000   Min.   :  1.00   Min.   :1.000  
##  1st Qu.:5.000   1st Qu.:5.750   1st Qu.:  2.00   1st Qu.:2.000  
##  Median :6.000   Median :7.000   Median :  5.00   Median :4.000  
##  Mean   :5.361   Mean   :6.167   Mean   : 31.83   Mean   :3.944  
##  3rd Qu.:6.000   3rd Qu.:7.000   3rd Qu.:  6.00   3rd Qu.:6.000  
##  Max.   :7.000   Max.   :7.000   Max.   :999.00   Max.   :7.000  
##      Item28          Item29         Item30           Item31     
##  Min.   :2.000   Min.   :1.00   Min.   :  1.00   Min.   :2.000  
##  1st Qu.:6.000   1st Qu.:5.75   1st Qu.:  4.00   1st Qu.:6.000  
##  Median :6.000   Median :6.00   Median :  6.00   Median :6.500  
##  Mean   :5.944   Mean   :5.75   Mean   : 32.69   Mean   :6.083  
##  3rd Qu.:7.000   3rd Qu.:7.00   3rd Qu.:  7.00   3rd Qu.:7.000  
##  Max.   :7.000   Max.   :7.00   Max.   :999.00   Max.   :7.000  
##      Item32           Item33          Item34           Item35     
##  Min.   :  3.00   Min.   :4.000   Min.   :  1.00   Min.   :1.000  
##  1st Qu.:  5.75   1st Qu.:6.000   1st Qu.:  2.75   1st Qu.:6.000  
##  Median :  6.00   Median :7.000   Median :  5.00   Median :6.000  
##  Mean   : 33.58   Mean   :6.306   Mean   : 31.89   Mean   :5.972  
##  3rd Qu.:  7.00   3rd Qu.:7.000   3rd Qu.:  6.00   3rd Qu.:7.000  
##  Max.   :999.00   Max.   :7.000   Max.   :999.00   Max.   :7.000  
##      item36           Item37          Item38           Item39     
##  Min.   :  1.00   Min.   :1.000   Min.   :  1.00   Min.   :1.000  
##  1st Qu.:  2.00   1st Qu.:5.000   1st Qu.:  3.50   1st Qu.:2.000  
##  Median :  4.00   Median :6.500   Median :  5.00   Median :4.000  
##  Mean   : 31.33   Mean   :5.806   Mean   : 31.97   Mean   :4.278  
##  3rd Qu.:  5.00   3rd Qu.:7.000   3rd Qu.:  6.00   3rd Qu.:7.000  
##  Max.   :999.00   Max.   :7.000   Max.   :999.00   Max.   :7.000  
##      Item40           Item41          Item42           Item43     
##  Min.   :  1.00   Min.   :1.000   Min.   :  1.00   Min.   :3.000  
##  1st Qu.:  1.00   1st Qu.:6.000   1st Qu.:  5.00   1st Qu.:6.000  
##  Median :  2.00   Median :6.500   Median :  6.00   Median :7.000  
##  Mean   : 30.03   Mean   :6.167   Mean   : 60.64   Mean   :6.111  
##  3rd Qu.:  3.25   3rd Qu.:7.000   3rd Qu.:  7.00   3rd Qu.:7.000  
##  Max.   :999.00   Max.   :7.000   Max.   :999.00   Max.   :7.000  
##      Item44           Item45         Item46           Item47     
##  Min.   :  1.00   Min.   :1.00   Min.   :  1.00   Min.   :1.000  
##  1st Qu.:  5.00   1st Qu.:4.00   1st Qu.:  4.00   1st Qu.:4.000  
##  Median :  6.00   Median :6.00   Median :  6.00   Median :6.000  
##  Mean   : 33.19   Mean   :5.25   Mean   : 32.97   Mean   :5.167  
##  3rd Qu.:  7.00   3rd Qu.:7.00   3rd Qu.:  7.00   3rd Qu.:7.000  
##  Max.   :999.00   Max.   :7.00   Max.   :999.00   Max.   :7.000  
##      Item48           Item49          Item50          Item51     
##  Min.   :  2.00   Min.   :1.000   Min.   :1.000   Min.   :2.000  
##  1st Qu.:  6.00   1st Qu.:2.750   1st Qu.:2.000   1st Qu.:5.000  
##  Median :  7.00   Median :5.000   Median :5.000   Median :6.000  
##  Mean   : 33.89   Mean   :4.417   Mean   :3.861   Mean   :5.639  
##  3rd Qu.:  7.00   3rd Qu.:6.000   3rd Qu.:5.250   3rd Qu.:7.000  
##  Max.   :999.00   Max.   :7.000   Max.   :6.000   Max.   :7.000  
##      Item52           Item53          Item54     
##  Min.   :  2.00   Min.   :5.000   Min.   :1.000  
##  1st Qu.:  6.00   1st Qu.:6.000   1st Qu.:4.000  
##  Median :  6.00   Median :6.000   Median :5.000  
##  Mean   : 33.69   Mean   :6.361   Mean   :5.028  
##  3rd Qu.:  7.00   3rd Qu.:7.000   3rd Qu.:6.000  
##  Max.   :999.00   Max.   :7.000   Max.   :7.000
head(sample)
##      ID Institution Deg_Prog Semester Age Gender Mother_Tong No_of_Lang
## 194 194           1        2        4  23      1           1          6
## 90   90           2        3        4  22      1           2          3
## 80   80           2        3        4  20      1           2          5
## 91   91           2        3        4  23      1           1          3
## 174 174           1        1        1  21      1           1          3
## 197 197           1        1        4  24      2           1          3
##     Spk_prof_Urdu Spk_prof_Eng Spk_prof_Pash Spk_prof_Balo Spk_prof_Brah
## 194             1            1             1             1             1
## 90              1            1             0             1             0
## 80              1            1             0             1             1
## 91              1            1             1             0             0
## 174             1            1             1             0             0
## 197             1            1             1             0             0
##     Spk_prof_Sind Spk_prof_Sara Spk_prof_Pers Spk_prof_Punj Spk_prof_Hind
## 194             0             0             1             0             0
## 90              0             0             0             0             0
## 80              1             0             0             0             0
## 91              0             0             0             0             0
## 174             0             0             0             0             0
## 197             0             0             0             0             0
##     Spk_prof_Other NameOtherLang Lang_Aca_Ex Sp_Slf_As Rd_Slf_As Wr_Slf_As
## 194              0                         0         2         1         2
## 90               0                         1         2         2         2
## 80               0                         1         2         2         3
## 91               0                         0         3         2         2
## 174              0                         1         3         2         2
## 197              0                         0         1         1         1
##     Lis_Slf_As Item1 Item2 Item3 Item4 Item5 Item6 Item7 Item8 Item9 Item10
## 194          2     2     5     7     5     5     3     6     6     5      2
## 90           2     4     7     6     6     7     5     7     6     7      7
## 80           3     6     7     7     4     6     3     6     5     7      7
## 91           3     1     6     7     5     7     4     6     6     7      3
## 174          1     1     2     7     5     7     7     4     6     6      7
## 197          2     3     1     3     7     6     3     6     6     7      7
##     Item11 Item12 Item13 Item14 Item15 Item16 Item17 Item18 Item19 Item20
## 194      4      2      6      5      6      3      1      1      5      6
## 90       1      6      7      5      1      7      2      7      6      3
## 80       1      1      4      7      2      7      2      7      4      2
## 91       7      6      5      7      2      5      3      6      5      1
## 174      5      3      6      3      7      6      5      7      2      5
## 197      1      5      4      7      7      7      7      1      7      7
##     Item21 Item22 Item23 Item24 Item25 Item26 Item27 Item28 Item29 Item30
## 194      4      2      6      3      6      2      2      2      2      1
## 90       6      7      5      4      4      2      5      6      6      6
## 80       2      6      7      2      4      1      6      1      7      7
## 91       1      4      6      2      6      5      1      6      5      5
## 174      7      6      7      1      6      4      1      7      7      5
## 197      7      4      7      7      7      2      5      7      7      4
##     Item31 Item32 Item33 Item34 Item35 item36 Item37 Item38 Item39 Item40
## 194      5      6      6      3      6      7      2      2      2      4
## 90       7      6      7      3      7      1      6      2      3      4
## 80       5      6      2      4      7      5      6      2      6      2
## 91       5      3      6      6      6      3      4      4      4      1
## 174      7      7      7      6      6      1      7      4      7      1
## 197      7      7      7      6      7      5      7      2      6      1
##     Item41 Item42 Item43 Item44 Item45 Item46 Item47 Item48 Item49 Item50
## 194      5      3      3      3      6      6      6      6      7      6
## 90       7      6      5      4      6      6      6      6      1      6
## 80       5      2      6      5      3      6      6      6      4      1
## 91       6      1      3      4      4      4      5      4      1      4
## 174      7      7      6      4      5      4      7      1      5      5
## 197      6      7      7      7      7      4      1      7      4      1
##     Item51 Item52 Item53 Item54
## 194      6      6      6      2
## 90       6      7      7      7
## 80       7      7      6      2
## 91       6      6      6      4
## 174      7      6      5      6
## 197      3      7      7      5
head(sample2)
##      ID Institution Deg_Prog Semester Age Gender Mother_Tong No_of_Lang
## 221 221           1        2        1  19      1           5          3
## 161 161           1        1        1  22      1           4          5
## 137 137           2        4        2  19      1           2          3
## 10   10           3        6        5  22      1           6          3
## 50   50           3        9        5  20      1          11          4
## 8     8           3        7        1  19      2           6          3
##     Spk_prof_Urdu Spk_prof_Eng Spk_prof_Pash Spk_prof_Balo Spk_prof_Brah
## 221             1            1             0             0             0
## 161             1            1             1             0             0
## 137             1            1             0             1             0
## 10              1            1             0             0             0
## 50              1            1             0             0             1
## 8               1            1             0             0             0
##     Spk_prof_Sind Spk_prof_Sara Spk_prof_Pers Spk_prof_Punj Spk_prof_Hind
## 221             0             0             0             1             0
## 161             0             0             0             1             1
## 137             0             0             0             0             0
## 10              0             0             1             0             0
## 50              1             0             0             0             0
## 8               0             0             1             0             0
##     Spk_prof_Other NameOtherLang Lang_Aca_Ex Sp_Slf_As Rd_Slf_As Wr_Slf_As
## 221              0                         1         1         2         2
## 161              0                         1         2         3         2
## 137              0                         1         2         2         2
## 10               0                         1         2         1         2
## 50               0                         0       999       999       999
## 8                0                         1         1         1         2
##     Lis_Slf_As Item1 Item2 Item3 Item4 Item5 Item6 Item7 Item8 Item9 Item10
## 221          1     7     7     7     6     7     1     6     5     6      2
## 161          2     1     2     7     2     4     3     6     5     7      5
## 137          2     7     6     7     6     6     3     6     5     6      3
## 10           2     5     4     7     6     7     2     7     7     7      1
## 50         999     6     2     1     1     6     2     1     6     6      1
## 8            1     1     6     7     6     6     4     6     4     6      6
##     Item11 Item12 Item13 Item14 Item15 Item16 Item17 Item18 Item19 Item20
## 221      7      1      2      7      7      6      6      6      7      7
## 161      5      4      6      5      2      6      6      6      6      7
## 137      7      5      7      1      7      6      5      7      7      7
## 10       3      4      7      1      7      7      4      4      7      7
## 50       2      6      6      2      1      1      1      2      6      2
## 8        1      4      6      6      6      6      4      4      4      6
##     Item21 Item22 Item23 Item24 Item25 Item26 Item27 Item28 Item29 Item30
## 221      1      6      6      5      7      6      2      7      7      1
## 161      5      4      7      4      6      6      6      7      7      6
## 137      6      5      7      2      7      6      1      7      6      7
## 10       7      7      7      7      7      7      1      7      7      7
## 50       2      6      6      6      2      3      2      4      2      2
## 8        7      6      6      6      6      2      2      6      6      6
##     Item31 Item32 Item33 Item34 Item35 item36 Item37 Item38 Item39 Item40
## 221      6      6      7      6      6      7      7      6      1      2
## 161      6      6      7      4      5      7      7      5      4      1
## 137      7      6      5      7      6      2      6      5      4      3
## 10       7      4      7      5      7      1      7      6      7      7
## 50       6      6      6      2      5      4      2      6      1      3
## 8        7      6      6      1      7      4      4      2      7      2
##     Item41 Item42 Item43 Item44 Item45 Item46 Item47 Item48 Item49 Item50
## 221      1      7      7      7      6      7      7      7      6      6
## 161      7      7      7      4      4      5      3      6      4      5
## 137      7      6      6      6      4      4      6      7      6      6
## 10       7      7      7      7      7      7      7      7      7      5
## 50       7      6      3      4      3      3      6      6      2      3
## 8        6      6      6      6      6      6      6      7      6      1
##     Item51 Item52 Item53 Item54
## 221      2      7      6      6
## 161      6      7      7      5
## 137      6      5      6      7
## 10       7      7      7      4
## 50       4    999      6      6
## 8        7      6      6      6
table(sample$Gender)
## 
##  1  2 
## 21 15
table(sample2$Gender)
## 
##  1  2 
## 21 15
cor(sample[,c("Item16", "Mother_Tong", "Age","Item3","Item7", "Item8", "Item48", "Item49", "Item52", "Item54")])
##                  Item16  Mother_Tong          Age        Item3        Item7
## Item16       1.00000000  0.108638866 -0.037260472 -0.167716539  0.396187423
## Mother_Tong  0.10863887  1.000000000 -0.007933954 -0.063457724 -0.058158925
## Age         -0.03726047 -0.007933954  1.000000000 -0.272404673 -0.120648386
## Item3       -0.16771654 -0.063457724 -0.272404673  1.000000000  0.031602401
## Item7        0.39618742 -0.058158925 -0.120648386  0.031602401  1.000000000
## Item8        0.38459306  0.231114460  0.174514798 -0.043704640  0.405685855
## Item48       0.08476510  0.138402615 -0.149454909 -0.003186459  0.321571796
## Item49       0.14854099  0.022020299 -0.313007754 -0.028357727  0.362953298
## Item52      -0.04461150  0.096349272 -0.152232441 -0.202986427 -0.001587372
## Item54       0.55253446  0.201411959  0.094757843  0.064200269  0.430577803
##                   Item8       Item48      Item49       Item52     Item54
## Item16       0.38459306  0.084765102  0.14854099 -0.044611501 0.55253446
## Mother_Tong  0.23111446  0.138402615  0.02202030  0.096349272 0.20141196
## Age          0.17451480 -0.149454909 -0.31300775 -0.152232441 0.09475784
## Item3       -0.04370464 -0.003186459 -0.02835773 -0.202986427 0.06420027
## Item7        0.40568586  0.321571796  0.36295330 -0.001587372 0.43057780
## Item8        1.00000000  0.085945640  0.09499393  0.177125455 0.66224930
## Item48       0.08594564  1.000000000  0.12763224  0.213352141 0.10126756
## Item49       0.09499393  0.127632240  1.00000000  0.030105398 0.20189573
## Item52       0.17712546  0.213352141  0.03010540  1.000000000 0.16387567
## Item54       0.66224930  0.101267556  0.20189573  0.163875672 1.00000000
cor(sample2[,c("Item16", "Mother_Tong", "Age","Item3","Item7", "Item8", "Item48", "Item49", "Item52", "Item54")])
##                  Item16 Mother_Tong         Age       Item3        Item7
## Item16       1.00000000 -0.13637086  0.99991903 -0.12013014 -0.028317425
## Mother_Tong -0.13637086  1.00000000 -0.13507353 -0.28673329 -0.276432803
## Age          0.99991903 -0.13507353  1.00000000 -0.12275420 -0.036730802
## Item3       -0.12013014 -0.28673329 -0.12275420  1.00000000  0.269850234
## Item7       -0.02831742 -0.27643280 -0.03673080  0.26985023  1.000000000
## Item8        0.10127112 -0.02844238  0.10276437 -0.03027508  0.003193161
## Item48       0.99995584 -0.13551698  0.99992221 -0.12289281 -0.032454027
## Item49      -0.03342915  0.02847840 -0.03957423  0.09528588  0.472023722
## Item52      -0.03776392  0.42697565 -0.03355282 -0.56673640 -0.437716747
## Item54      -0.11084009  0.11088094 -0.11247319  0.20984828  0.264496654
##                    Item8      Item48      Item49      Item52       Item54
## Item16       0.101271124  0.99995584 -0.03342915 -0.03776392 -0.110840086
## Mother_Tong -0.028442378 -0.13551698  0.02847840  0.42697565  0.110880941
## Age          0.102764371  0.99992221 -0.03957423 -0.03355282 -0.112473193
## Item3       -0.030275078 -0.12289281  0.09528588 -0.56673640  0.209848282
## Item7        0.003193161 -0.03245403  0.47202372 -0.43771675  0.264496654
## Item8        1.000000000  0.10206506 -0.15812645  0.09938337 -0.009986593
## Item48       0.102065057  1.00000000 -0.03447422 -0.03314801 -0.111617808
## Item49      -0.158126446 -0.03447422  1.00000000 -0.20563377  0.204114360
## Item52       0.099383372 -0.03314801 -0.20563377  1.00000000  0.106273942
## Item54      -0.009986593 -0.11161781  0.20411436  0.10627394  1.000000000
par(mfrow = c(1, 2))
hist(sample$Item16)
boxplot(sample$Item16)

hist(sample$Age)
boxplot(sample$Age)

#hist(sample$Gender)
#boxplot(sample$Gender)
hist(sample$Item3)
boxplot(sample$Item3)

hist(sample$Item7)
boxplot(sample$Item7)

hist(sample$Item8)
boxplot(sample$Item8)

hist(sample$Item48)
boxplot(sample$Item48)

hist(sample$Item49)
boxplot(sample$Item49)

hist(sample$Item52)
boxplot(sample$Item52)

hist(sample$Item54)
boxplot(sample$Item54)

par(mfrow = c(1, 2))
hist(sample2$Item16)
boxplot(sample2$Item16)

hist(sample2$Age)
boxplot(sample2$Age)

#hist(sample$Gender)
#boxplot(sample$Gender)
hist(sample2$Item3)
boxplot(sample2$Item3)

hist(sample2$Item7)
boxplot(sample2$Item7)

hist(sample2$Item8)
boxplot(sample2$Item8)

hist(sample2$Item48)
boxplot(sample2$Item48)

hist(sample2$Item49)
boxplot(sample2$Item49)

hist(sample2$Item52)
boxplot(sample2$Item52)

hist(sample2$Item54)
boxplot(sample2$Item54)

summary(m0 <- lm(Item16 ~ Age, data = sample))
## 
## Call:
## lm(formula = Item16 ~ Age, data = sample)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3.03016 -0.33028 -0.00153  0.96984  1.05575 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  6.63154    2.78330   2.383   0.0229 *
## Age         -0.02864    0.13172  -0.217   0.8292  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.123 on 34 degrees of freedom
## Multiple R-squared:  0.001388,   Adjusted R-squared:  -0.02798 
## F-statistic: 0.04727 on 1 and 34 DF,  p-value: 0.8292
summary(m1 <- lm(Item16 ~ Age + Gender, data = sample))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender, data = sample)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.90476 -0.44442  0.09524  0.93127  1.13115 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  6.65891    2.79904   2.379   0.0233 *
## Age         -0.03591    0.13277  -0.270   0.7885  
## Gender2      0.30242    0.38283   0.790   0.4352  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.13 on 33 degrees of freedom
## Multiple R-squared:  0.01992,    Adjusted R-squared:  -0.03948 
## F-statistic: 0.3354 on 2 and 33 DF,  p-value: 0.7175
AIC(m0) - AIC(m1)
## [1] -1.325603
summary(m2 <- lm(Item16 ~ Age + Gender + Item3, data = sample))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3, data = sample)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.8387 -0.4538  0.1248  1.0061  1.2343 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  8.99003    3.63255   2.475   0.0188 *
## Age         -0.07297    0.13775  -0.530   0.6000  
## Gender2      0.26798    0.38428   0.697   0.4906  
## Item3       -0.23129    0.22979  -1.007   0.3217  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.129 on 32 degrees of freedom
## Multiple R-squared:   0.05,  Adjusted R-squared:  -0.03907 
## F-statistic: 0.5614 on 3 and 32 DF,  p-value: 0.6444
AIC(m1) - AIC(m2)
## [1] -0.8779507
summary(m3 <- lm(Item16 ~ Age + Gender + Item3 + Item7, data=sample))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3 + Item7, data = sample)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.9213 -0.8489  0.1313  0.7150  1.4862 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  6.26157    3.60208   1.738   0.0921 .
## Age         -0.03227    0.13033  -0.248   0.8061  
## Gender2      0.01289    0.37661   0.034   0.9729  
## Item3       -0.24418    0.21550  -1.133   0.2659  
## Item7        0.35185    0.15131   2.325   0.0268 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.059 on 31 degrees of freedom
## Multiple R-squared:  0.1911, Adjusted R-squared:  0.08671 
## F-statistic: 1.831 on 4 and 31 DF,  p-value: 0.148
AIC(m2) - AIC(m3)
## [1] 3.787858
summary(m4 <- lm(Item16 ~ Age + Gender + Item3 + Item7 + Item8, data=sample))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3 + Item7 + Item8, data = sample)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.8434 -0.6731  0.3032  0.6863  1.5421 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  7.31319    3.54741   2.062   0.0480 *
## Age         -0.09513    0.13162  -0.723   0.4754  
## Gender2      0.24010    0.38857   0.618   0.5413  
## Item3       -0.23409    0.20913  -1.119   0.2719  
## Item7        0.20087    0.17112   1.174   0.2497  
## Item8        0.19193    0.11183   1.716   0.0964 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.027 on 30 degrees of freedom
## Multiple R-squared:  0.2634, Adjusted R-squared:  0.1406 
## F-statistic: 2.146 on 5 and 30 DF,  p-value: 0.08706
AIC(m3) - AIC(m4)
## [1] 1.371938
summary(m5 <- lm(Item16 ~ Age + Gender + Item3 + Item7 + Item8 + Item48, data=sample))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48, data = sample)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.8428 -0.7096  0.2147  0.6933  1.5850 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  7.69621    3.78504   2.033   0.0513 .
## Age         -0.10063    0.13467  -0.747   0.4609  
## Gender2      0.24682    0.39500   0.625   0.5370  
## Item3       -0.23708    0.21250  -1.116   0.2737  
## Item7        0.21546    0.17930   1.202   0.2392  
## Item8        0.19178    0.11353   1.689   0.1019  
## Item48      -0.05379    0.16357  -0.329   0.7447  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.043 on 29 degrees of freedom
## Multiple R-squared:  0.2662, Adjusted R-squared:  0.1143 
## F-statistic: 1.753 on 6 and 29 DF,  p-value: 0.1443
AIC(m4) - AIC(m5)
## [1] -1.866026
summary(m6 <- lm(Item16 ~ Age + Gender + Item3 + Item7 + Item8 + Item48 + Item49, data=sample))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48 + Item49, data = sample)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.7981 -0.7037  0.2120  0.6855  1.6026 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  7.90009    4.08998   1.932   0.0636 .
## Age         -0.10727    0.14416  -0.744   0.4630  
## Gender2      0.24897    0.40210   0.619   0.5408  
## Item3       -0.24125    0.21801  -1.107   0.2779  
## Item7        0.22313    0.18963   1.177   0.2493  
## Item8        0.19217    0.11552   1.663   0.1074  
## Item48      -0.05456    0.16648  -0.328   0.7456  
## Item49      -0.01577    0.10666  -0.148   0.8835  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.061 on 28 degrees of freedom
## Multiple R-squared:  0.2667, Adjusted R-squared:  0.0834 
## F-statistic: 1.455 on 7 and 28 DF,  p-value: 0.2237
AIC(m5) - AIC(m6)
## [1] -1.971904
summary(m7 <- lm(Item16 ~ Age + Gender + Item3 + Item7 + Item8 + Item48 + Item49 + Item52, data=sample))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48 + Item49 + Item52, data = sample)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.7995 -0.6672  0.1284  0.7512  1.3917 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 10.43956    4.85975   2.148   0.0408 *
## Age         -0.14472    0.14939  -0.969   0.3413  
## Gender2      0.25124    0.40253   0.624   0.5378  
## Item3       -0.29943    0.22633  -1.323   0.1970  
## Item7        0.19310    0.19234   1.004   0.3243  
## Item8        0.22122    0.11946   1.852   0.0750 .
## Item48      -0.01848    0.17076  -0.108   0.9146  
## Item49      -0.02075    0.10690  -0.194   0.8475  
## Item52      -0.24089    0.24834  -0.970   0.3407  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.062 on 27 degrees of freedom
## Multiple R-squared:  0.2914, Adjusted R-squared:  0.08147 
## F-statistic: 1.388 on 8 and 27 DF,  p-value: 0.2462
AIC(m6) - AIC(m7)
## [1] -0.7668086
AIC(m2) - AIC(m7)
## [1] 0.5550568
summary(m8 <- lm(Item16 ~ Age + Gender + Item3 + Item7 + Item8 + Item48 + Item49 + Item52 + Item54, data=sample))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48 + Item49 + Item52 + Item54, data = sample)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.6630 -0.7043  0.1256  0.5801  1.9643 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 12.5057150  4.4430289   2.815  0.00918 **
## Age         -0.1808285  0.1352028  -1.337  0.19266   
## Gender2      0.0512890  0.3700025   0.139  0.89082   
## Item3       -0.4101342  0.2079160  -1.973  0.05926 . 
## Item7        0.1344454  0.1745763   0.770  0.44817   
## Item8        0.0173940  0.1314257   0.132  0.89573   
## Item48       0.0008866  0.1539504   0.006  0.99545   
## Item49      -0.0593606  0.0973270  -0.610  0.54722   
## Item52      -0.3304971  0.2260984  -1.462  0.15579   
## Item54       0.3347334  0.1239762   2.700  0.01203 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9564 on 26 degrees of freedom
## Multiple R-squared:  0.4466, Adjusted R-squared:  0.255 
## F-statistic: 2.331 on 9 and 26 DF,  p-value: 0.0444
AIC(m7) - AIC(m8)
## [1] 6.897672
AIC(m3) - AIC(m8)
## [1] 3.664871
summary(ms2_0 <- lm(Item16 ~ Age, data=sample2))
## 
## Call:
## lm(formula = Item16 ~ Age, data = sample2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.0930 -2.1233  0.0047  1.9260  2.9525 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -15.225245   0.371670  -40.96   <2e-16 ***
## Age           1.015153   0.002216  458.19   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.137 on 34 degrees of freedom
## Multiple R-squared:  0.9998, Adjusted R-squared:  0.9998 
## F-statistic: 2.099e+05 on 1 and 34 DF,  p-value: < 2.2e-16
summary(ms2_1 <- lm(Item16 ~ Age + Gender, data=sample2))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender, data = sample2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.2271 -1.8997 -0.0698  1.8778  2.8037 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -15.080532   0.474000 -31.815   <2e-16 ***
## Age           1.015382   0.002287 444.077   <2e-16 ***
## Gender2      -0.373602   0.745674  -0.501     0.62    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.161 on 33 degrees of freedom
## Multiple R-squared:  0.9998, Adjusted R-squared:  0.9998 
## F-statistic: 1.027e+05 on 2 and 33 DF,  p-value: < 2.2e-16
AIC(ms2_0) - AIC(ms2_1)
## [1] -1.727189
summary(ms2_2 <- lm(Item16 ~ Age + Gender + Item3, data=sample2))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3, data = sample2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.9272 -1.6122  0.1402  1.6697  3.4614 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -16.817344   1.616874 -10.401 8.59e-12 ***
## Age           1.015599   0.002286 444.335  < 2e-16 ***
## Gender2      -0.211904   0.756563  -0.280    0.781    
## Item3         0.271483   0.241721   1.123    0.270    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.153 on 32 degrees of freedom
## Multiple R-squared:  0.9998, Adjusted R-squared:  0.9998 
## F-statistic: 6.898e+04 on 3 and 32 DF,  p-value: < 2.2e-16
AIC(ms2_1) - AIC(ms2_2)
## [1] -0.6081615
summary(ms2_3 <- lm(Item16 ~ Age + Gender + Item3 + Item7, data=sample2))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3 + Item7, data = sample2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8332 -1.0203  0.2429  0.9663  2.2488 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -19.588067   1.381294 -14.181 4.27e-15 ***
## Age           1.015723   0.001769 574.163  < 2e-16 ***
## Gender2      -0.383447   0.586618  -0.654    0.518    
## Item3         0.019087   0.194509   0.098    0.922    
## Item7         0.821003   0.173351   4.736 4.57e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.666 on 31 degrees of freedom
## Multiple R-squared:  0.9999, Adjusted R-squared:  0.9999 
## F-statistic: 8.639e+04 on 4 and 31 DF,  p-value: < 2.2e-16
AIC(ms2_2) - AIC(ms2_3)
## [1] 17.59813
summary(ms2_4 <- lm(Item16 ~ Age + Gender + Item3 + Item7 + Item8, data=sample2))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3 + Item7 + Item8, data = sample2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8151 -0.8680  0.5295  1.0166  2.3958 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -18.781994   1.617253 -11.614 1.26e-12 ***
## Age           1.015916   0.001783 569.918  < 2e-16 ***
## Gender2      -0.428449   0.589196  -0.727    0.473    
## Item3         0.012332   0.194873   0.063    0.950    
## Item7         0.823870   0.173588   4.746 4.77e-05 ***
## Item8        -0.154977   0.161187  -0.961    0.344    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.668 on 30 degrees of freedom
## Multiple R-squared:  0.9999, Adjusted R-squared:  0.9999 
## F-statistic: 6.894e+04 on 5 and 30 DF,  p-value: < 2.2e-16
AIC(ms2_3) - AIC(ms2_4)
## [1] -0.9074324
summary(ms2_5 <- lm(Item16 ~ Age + Gender + Item3 + Item7 + Item8 + Item48, data=sample2))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48, data = sample2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.6007 -0.3932  0.0265  0.6465  1.7749 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -9.16964    1.97999  -4.631 7.06e-05 ***
## Age          0.41224    0.10288   4.007 0.000393 ***
## Gender2     -0.66994    0.40728  -1.645 0.110785    
## Item3        0.08671    0.13461   0.644 0.524542    
## Item7        0.55678    0.12776   4.358 0.000150 ***
## Item8       -0.11799    0.11103  -1.063 0.296678    
## Item48       0.59509    0.10141   5.868 2.29e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.147 on 29 degrees of freedom
## Multiple R-squared:      1,  Adjusted R-squared:      1 
## F-statistic: 1.215e+05 on 6 and 29 DF,  p-value: < 2.2e-16
AIC(ms2_4) - AIC(ms2_5)
## [1] 26.17687
AIC(ms2_3) - AIC(ms2_5)
## [1] 25.26944
summary(ms2_6 <- lm(Item16 ~ Age + Gender + Item3 + Item7 + Item8 + Item48 + Item49, data=sample2))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48 + Item49, data = sample2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.5735 -0.3797  0.0001  0.6846  1.7706 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -8.98898    2.23713  -4.018  0.00040 ***
## Age          0.40561    0.11058   3.668  0.00102 ** 
## Gender2     -0.69191    0.43085  -1.606  0.11951    
## Item3        0.08502    0.13722   0.620  0.54055    
## Item7        0.56732    0.14183   4.000  0.00042 ***
## Item8       -0.12216    0.11514  -1.061  0.29777    
## Item48       0.60163    0.10902   5.519 6.73e-06 ***
## Item49      -0.02288    0.12339  -0.185  0.85424    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.167 on 28 degrees of freedom
## Multiple R-squared:      1,  Adjusted R-squared:      1 
## F-statistic: 1.007e+05 on 7 and 28 DF,  p-value: < 2.2e-16
AIC(ms2_5) - AIC(ms2_6)
## [1] -1.955825
summary(ms2_7 <- lm(Item16 ~ Age + Gender + Item3 + Item7 + Item8 + Item48 + Item49 + Item52, data=sample2))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48 + Item49 + Item52, data = sample2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3228 -0.4297  0.0191  0.6694  1.7005 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -5.890615   2.544035  -2.315  0.02842 *  
## Age          0.339702   0.108322   3.136  0.00411 ** 
## Gender2     -1.033796   0.434742  -2.378  0.02475 *  
## Item3       -0.116715   0.159143  -0.733  0.46964    
## Item7        0.462615   0.141834   3.262  0.00300 ** 
## Item8       -0.100780   0.108690  -0.927  0.36203    
## Item48       0.666367   0.106757   6.242 1.12e-06 ***
## Item49      -0.066298   0.117721  -0.563  0.57796    
## Item52      -0.003519   0.001626  -2.164  0.03945 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.097 on 27 degrees of freedom
## Multiple R-squared:      1,  Adjusted R-squared:      1 
## F-statistic: 9.967e+04 on 8 and 27 DF,  p-value: < 2.2e-16
AIC(ms2_6) - AIC(ms2_7)
## [1] 3.759547
AIC(ms2_5) - AIC(ms2_7)
## [1] 1.803722
summary(ms2_8 <- lm(Item16 ~ Age + Gender + Item3 + Item7 + Item8 + Item48 + Item49 + Item52 + Item54, data=sample2))
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48 + Item49 + Item52 + Item54, data = sample2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3251 -0.5069  0.0008  0.6967  1.6478 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -5.329722   2.627812  -2.028  0.05290 .  
## Age          0.316550   0.111700   2.834  0.00877 ** 
## Gender2     -1.182343   0.466397  -2.535  0.01760 *  
## Item3       -0.188795   0.178628  -1.057  0.30027    
## Item7        0.417730   0.150802   2.770  0.01021 *  
## Item8       -0.100009   0.109075  -0.917  0.36763    
## Item48       0.689274   0.110109   6.260 1.26e-06 ***
## Item49      -0.094705   0.122271  -0.775  0.44559    
## Item52      -0.004377   0.001889  -2.317  0.02866 *  
## Item54       0.131902   0.146434   0.901  0.37599    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.101 on 26 degrees of freedom
## Multiple R-squared:      1,  Adjusted R-squared:      1 
## F-statistic: 8.797e+04 on 9 and 26 DF,  p-value: < 2.2e-16
AIC(ms2_7) - AIC(ms2_8)
## [1] -0.8937452
library(visreg)  
par(mfrow = c(2, 2))
visreg(m8)

library(visreg) 
par(mfrow = c(2, 2))
visreg(ms2_5)

# linearity
library(car)  
## Loading required package: carData
par(mfrow = c(1, 3))
crPlot(m8, var = "Age")  
crPlot(m8, var = "Gender")
crPlot(m8, var = "Item3")

crPlot(m8, var = "Item7")  
crPlot(m8, var = "Item8")
crPlot(m8, var = "Item48")

crPlot(m8, var = "Item49")  
crPlot(m8, var = "Item52")
crPlot(m8, var = "Item54")

# linearity
library(car)  
par(mfrow = c(1, 3))
crPlot(ms2_5, var = "Age")  
crPlot(ms2_5, var = "Gender")
crPlot(ms2_5, var = "Item3")

crPlot(ms2_5, var = "Item7")
crPlot(ms2_5, var = "Item8")
crPlot(ms2_5, var = "Item48")

par(mfrow = c(1, 1))

# autocorrelation in residuals: 
acf(resid(m8))

par(mfrow = c(1, 1))

# autocorrelation in residuals: 
acf(resid(ms2_5))

# multicollinearity: 
car::vif(m8)  
##      Age   Gender    Item3    Item7    Item8   Item48   Item49   Item52 
## 1.453910 1.309636 1.243245 1.809457 2.297028 1.197693 1.314949 1.260613 
##   Item54 
## 2.083683
# multicollinearity: for Age and Item48, the (G)VIF > 5 - violated
car::vif(ms2_5)  
##         Age      Gender       Item3       Item7       Item8      Item48 
## 7485.760893    1.102994    1.150629    1.240448    1.020859 7488.135325
# homoscedasticity: 
plot(fitted(m8), resid(m8))

# homoscedasticity: 
plot(fitted(ms2_5), resid(ms2_5))

# significant heteroscedasticity (p-value < 0.05)
ncvTest(m8)
## Non-constant Variance Score Test 
## Variance formula: ~ fitted.values 
## Chisquare = 6.395314, Df = 1, p = 0.011442
ncvTest(m2, ~Age)
## Non-constant Variance Score Test 
## Variance formula: ~ Age 
## Chisquare = 0.1992435, Df = 1, p = 0.65533
ncvTest(m2, ~Gender)
## Non-constant Variance Score Test 
## Variance formula: ~ Gender 
## Chisquare = 4.050853, Df = 1, p = 0.044149
ncvTest(m2, ~Item3)
## Non-constant Variance Score Test 
## Variance formula: ~ Item3 
## Chisquare = 2.090069, Df = 1, p = 0.14826
library(MASS)
MASS::boxcox(Item16 ~ Age + Gender + Item3 + Item7 + Item8 + Item48 + Item49 + Item52 + Item54, data=sample)

#library(moments)
#skewness(sample$Item3, na.rm = TRUE)
#sample$Item3.transformSkew <- log10(max(sample$Item3+1) - sample$Item3)
sample$Item16.1.75 <- sample$Item16^1.75
m8 <- lm(Item16.1.75 ~ Age + Gender + Item3 + Item7 + Item8 + Item48 + Item49 + Item52 + Item54, data=sample)
summary(m8)
## 
## Call:
## lm(formula = Item16.1.75 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48 + Item49 + Item52 + Item54, data = sample)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.9618 -4.8573  0.8645  3.9681 12.4404 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 60.18787   27.89523   2.158   0.0404 *
## Age         -1.01708    0.84886  -1.198   0.2417  
## Gender2      0.05651    2.32303   0.024   0.9808  
## Item3       -2.46764    1.30539  -1.890   0.0699 .
## Item7        0.74976    1.09606   0.684   0.5000  
## Item8        0.16754    0.82515   0.203   0.8407  
## Item48       0.22137    0.96657   0.229   0.8206  
## Item49      -0.34235    0.61106  -0.560   0.5801  
## Item52      -2.02678    1.41954  -1.428   0.1653  
## Item54       2.00191    0.77838   2.572   0.0162 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.005 on 26 degrees of freedom
## Multiple R-squared:  0.4282, Adjusted R-squared:  0.2303 
## F-statistic: 2.163 on 9 and 26 DF,  p-value: 0.06015
ncvTest(m8)
## Non-constant Variance Score Test 
## Variance formula: ~ fitted.values 
## Chisquare = 3.401818, Df = 1, p = 0.065125
# no significant heteroscedasticity (p-value > 0.05)
ncvTest(ms2_5)
## Non-constant Variance Score Test 
## Variance formula: ~ fitted.values 
## Chisquare = 0.5398767, Df = 1, p = 0.46248
ncvTest(ms2_5, ~Age)
## Non-constant Variance Score Test 
## Variance formula: ~ Age 
## Chisquare = 0.51511, Df = 1, p = 0.47294
ncvTest(ms2_5, ~Gender)
## Non-constant Variance Score Test 
## Variance formula: ~ Gender 
## Chisquare = 2.41587, Df = 1, p = 0.12011
ncvTest(ms2_5, ~Item3)
## Non-constant Variance Score Test 
## Variance formula: ~ Item3 
## Chisquare = 1.550242, Df = 1, p = 0.2131
ncvTest(ms2_5, ~Item7)
## Non-constant Variance Score Test 
## Variance formula: ~ Item7 
## Chisquare = 1.658469, Df = 1, p = 0.19781
ncvTest(ms2_5, ~Item48)
## Non-constant Variance Score Test 
## Variance formula: ~ Item48 
## Chisquare = 0.53593, Df = 1, p = 0.46412
shapiro.test(resid(m8))$p.value
## [1] 0.1394061
# distribution of residuals: 
qqnorm(resid(m8))
qqline(resid(m8))

shapiro.test(resid(ms2_5))$p.value
## [1] 0.05473277
# distribution of residuals: 
qqnorm(resid(ms2_5))
qqline(resid(ms2_5))

summary(m8)
## 
## Call:
## lm(formula = Item16.1.75 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48 + Item49 + Item52 + Item54, data = sample)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.9618 -4.8573  0.8645  3.9681 12.4404 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 60.18787   27.89523   2.158   0.0404 *
## Age         -1.01708    0.84886  -1.198   0.2417  
## Gender2      0.05651    2.32303   0.024   0.9808  
## Item3       -2.46764    1.30539  -1.890   0.0699 .
## Item7        0.74976    1.09606   0.684   0.5000  
## Item8        0.16754    0.82515   0.203   0.8407  
## Item48       0.22137    0.96657   0.229   0.8206  
## Item49      -0.34235    0.61106  -0.560   0.5801  
## Item52      -2.02678    1.41954  -1.428   0.1653  
## Item54       2.00191    0.77838   2.572   0.0162 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.005 on 26 degrees of freedom
## Multiple R-squared:  0.4282, Adjusted R-squared:  0.2303 
## F-statistic: 2.163 on 9 and 26 DF,  p-value: 0.06015
summary(m8) -> OLSreg1
coef=OLSreg1$coefficients[,1]
error=OLSreg1$coefficients[,2]  
ci1 <- list()
for (i in 1:length(coef)){
ci1[[i]] <- coef[i] + c(-1,1)*error[i]*qnorm(0.995)}
ci1
## [[1]]
## [1] -11.66547 132.04121
## 
## [[2]]
## [1] -3.203598  1.169442
## 
## [[3]]
## [1] -5.927226  6.040247
## 
## [[4]]
## [1] -5.8300938  0.8948058
## 
## [[5]]
## [1] -2.073514  3.573035
## 
## [[6]]
## [1] -1.957891  2.292981
## 
## [[7]]
## [1] -2.268340  2.711077
## 
## [[8]]
## [1] -1.916338  1.231637
## 
## [[9]]
## [1] -5.683279  1.629715
## 
## [[10]]
## [1] -0.003052942  4.006870563
ci5 <- list()
for (i in 1:length(coef)){
ci5[[i]] <- coef[i] + c(-1,1)*error[i]*qnorm(0.975)}
ci5
## [[1]]
## [1]   5.514235 114.861509
## 
## [[2]]
## [1] -2.6808139  0.6466586
## 
## [[3]]
## [1] -4.496550  4.609572
## 
## [[4]]
## [1] -5.02615226  0.09086426
## 
## [[5]]
## [1] -1.398486  2.898007
## 
## [[6]]
## [1] -1.449712  1.784802
## 
## [[7]]
## [1] -1.673066  2.115803
## 
## [[8]]
## [1] -1.5400068  0.8553063
## 
## [[9]]
## [1] -4.8090328  0.7554686
## 
## [[10]]
## [1] 0.4763214 3.5274962
ci10 <- list()
for (i in 1:length(coef)){
ci10[[i]] <- coef[i] + c(-1,1)*error[i]*qnorm(0.95)}
ci10
## [[1]]
## [1]  14.30431 106.07143
## 
## [[2]]
## [1] -2.4133291  0.3791739
## 
## [[3]]
## [1] -3.764539  3.877560
## 
## [[4]]
## [1] -4.6148118 -0.3204762
## 
## [[5]]
## [1] -1.053105  2.552626
## 
## [[6]]
## [1] -1.18970  1.52479
## 
## [[7]]
## [1] -1.368491  1.811228
## 
## [[8]]
## [1] -1.3474553  0.6627548
## 
## [[9]]
## [1] -4.3617205  0.3081563
## 
## [[10]]
## [1] 0.7215955 3.2822221
# Bootstrap OLS regression
library(boot)
## 
## Attaching package: 'boot'
## The following object is masked from 'package:car':
## 
##     logit
bs <- function(formula, data, indices) {
d <- data[indices,]  
   fit <- lm(formula, data=d)
   return(coef(fit)) 
 } 
Bootreg <-boot(data=sample,statistic=bs,R=1000, formula=Item16.1.75 ~ Age + Gender + Item3 + Item7 + Item8 + Item48 + Item49 + Item52 + Item54)
summary(Bootreg)
## 
## Number of bootstrap replications R = 1000 
##     original  bootBias   bootSE  bootMed
## 1  60.187872 -5.328387 34.81098 55.66312
## 2  -1.017078  0.151154  1.04714 -0.92964
## 3   0.056511 -0.227836  2.35701 -0.21967
## 4  -2.467644  0.251456  1.66829 -2.32203
## 5   0.749761  0.046124  1.41549  0.64732
## 6   0.167545  0.079677  0.98380  0.23233
## 7   0.221369 -0.094911  1.28520  0.24299
## 8  -0.342350  0.018686  0.76112 -0.35999
## 9  -2.026782  0.191227  1.47166 -1.88684
## 10  2.001909 -0.165543  1.11947  1.92084
pdf(file="/Users/trekkatkins/Downloads/7585259/figure1.pdf")
plot(Bootreg, index=1) # intercept 
plot(Bootreg, index=2) #
plot(Bootreg, index=3) # 
plot(Bootreg, index=4) # 
plot(Bootreg, index=5) #
plot(Bootreg, index=6) # 
plot(Bootreg, index=7) # 
plot(Bootreg, index=8) # 
boot.ci(Bootreg, type="perc", conf=c(0.90,0.95,0.99), index=1) # intercept 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 1)
## 
## Intervals : 
## Level     Percentile     
## 90%   ( -7.40, 110.82 )   
## 95%   (-18.27, 118.07 )   
## 99%   (-37.34, 136.13 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg, type="perc", conf=c(0.90,0.95,0.99), index=2) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 2)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-2.485,  0.982 )   
## 95%   (-2.741,  1.334 )   
## 99%   (-3.281,  2.138 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg, type="perc", conf=c(0.90,0.95,0.99), index=3) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 3)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-3.9039,  3.5967 )   
## 95%   (-4.7546,  4.3745 )   
## 99%   (-6.6174,  6.6767 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg, type="perc", conf=c(0.90,0.95,0.99), index=4) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 4)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-4.719,  0.690 )   
## 95%   (-5.290,  1.629 )   
## 99%   (-6.625,  3.652 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg, type="perc", conf=c(0.90,0.95,0.99), index=5) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 5)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-1.1894,  3.2401 )   
## 95%   (-1.7555,  3.7783 )   
## 99%   (-3.3102,  5.8444 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg, type="perc", conf=c(0.90,0.95,0.99), index=6) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 6)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-1.2208,  2.0133 )   
## 95%   (-1.4714,  2.3911 )   
## 99%   (-2.1298,  3.4004 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg, type="perc", conf=c(0.90,0.95,0.99), index=7) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 7)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-2.3417,  1.8792 )   
## 95%   (-3.2237,  2.3696 )   
## 99%   (-5.1745,  3.6594 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg, type="perc", conf=c(0.90,0.95,0.99), index=8) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 8)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-1.4446,  0.9700 )   
## 95%   (-1.7170,  1.4076 )   
## 99%   (-2.5678,  2.2237 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
dev.off
## function (which = dev.cur()) 
## {
##     if (which == 1) 
##         stop("cannot shut down device 1 (the null device)")
##     .External(C_devoff, as.integer(which))
##     dev.cur()
## }
## <bytecode: 0x7f9720ffc478>
## <environment: namespace:grDevices>
# Quantile regression 
library(quantreg)
## Loading required package: SparseM
## 
## Attaching package: 'SparseM'
## The following object is masked from 'package:base':
## 
##     backsolve
Qreg1 <- rq(Item16.1.75 ~ Age + Gender + Item3 + Item7 + Item8 + Item48 + Item49 + Item52 + Item54, tau = .5, data=sample)
summary(Qreg1, se="iid", bsmethod="xy")
## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique
## 
## Call: rq(formula = Item16.1.75 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48 + Item49 + Item52 + Item54, tau = 0.5, data = sample)
## 
## tau: [1] 0.5
## 
## Coefficients:
##             Value    Std. Error t value  Pr(>|t|)
## (Intercept) 31.73732 29.52183    1.07505  0.29223
## Age          0.20938  0.89836    0.23307  0.81753
## Gender2     -1.97082  2.45849   -0.80164  0.43003
## Item3       -1.72891  1.38150   -1.25147  0.22191
## Item7        0.22903  1.15998    0.19744  0.84502
## Item8       -0.06945  0.87326   -0.07953  0.93722
## Item48       1.00049  1.02293    0.97806  0.33706
## Item49       0.01728  0.64669    0.02672  0.97889
## Item52      -2.66503  1.50232   -1.77395  0.08779
## Item54       2.22899  0.82376    2.70586  0.01187
summary(Qreg1, se="iid", bsmethod="xy") -> Qreg2
## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique
coef=Qreg2$coefficients[,1] 
error=Qreg2$coefficients[,2]  
ci1 <- list()
for (i in 1:length(coef)){
ci1[[i]] <- coef[i] + c(-1,1)*error[i]*qnorm(0.995)}
ci1
## [[1]]
## [1] -44.30587 107.78052
## 
## [[2]]
## [1] -2.104638  2.523399
## 
## [[3]]
## [1] -8.303476  4.361835
## 
## [[4]]
## [1] -5.287433  1.829604
## 
## [[5]]
## [1] -2.758872  3.216935
## 
## [[6]]
## [1] -2.318828  2.179918
## 
## [[7]]
## [1] -1.634400  3.635374
## 
## [[8]]
## [1] -1.648490  1.683048
## 
## [[9]]
## [1] -6.534741  1.204683
## 
## [[10]]
## [1] 0.1071152 4.3508624
ci5 <- list()
for (i in 1:length(coef)){
ci5[[i]] <- coef[i] + c(-1,1)*error[i]*qnorm(0.975)}
ci5
## [[1]]
## [1] -26.12440  89.59905
## 
## [[2]]
## [1] -1.551370  1.970131
## 
## [[3]]
## [1] -6.789376  2.847735
## 
## [[4]]
## [1] -4.4366128  0.9787834
## 
## [[5]]
## [1] -2.044482  2.502545
## 
## [[6]]
## [1] -1.781016  1.642107
## 
## [[7]]
## [1] -1.004414  3.005388
## 
## [[8]]
## [1] -1.250214  1.284772
## 
## [[9]]
## [1] -5.6095162  0.2794582
## 
## [[10]]
## [1] 0.6144424 3.8435351
ci10 <- list()
for (i in 1:length(coef)){
ci10[[i]] <- coef[i] + c(-1,1)*error[i]*qnorm(0.95)}
ci10
## [[1]]
## [1] -16.82177  80.29641
## 
## [[2]]
## [1] -1.268288  1.687049
## 
## [[3]]
## [1] -6.014680  2.073039
## 
## [[4]]
## [1] -4.0012866  0.5434572
## 
## [[5]]
## [1] -1.678962  2.137024
## 
## [[6]]
## [1] -1.505842  1.366933
## 
## [[7]]
## [1] -0.6820792  2.6830532
## 
## [[8]]
## [1] -1.046435  1.080993
## 
## [[9]]
## [1] -5.1361206 -0.1939374
## 
## [[10]]
## [1] 0.8740188 3.5839588

Bootstrap Qunantile regression

library(quantreg) bs <- function(formula, data, indices) { d <- data[indices,]
fit <- rq(formula, tau=0.5, data=d) return(coef(fit)) } library(quantreg) library(boot) Bootreg <-boot(data=sample,statistic=bs,R=1000, formula=Item16.1.75 ~ Age + Gender + Item3 + Item7 + Item8 + Item48 + Item49 + Item52 + Item54) summary(Bootreg) pdf(file=“/Users/trekkatkins/Downloads/7585259/figure2.pdf”) plot(Bootreg, index=1) # intercept plot(Bootreg, index=2) # plot(Bootreg, index=3) # plot(Bootreg, index=4) #
plot(Bootreg, index=5) # plot(Bootreg, index=6) # plot(Bootreg, index=7) #
plot(Bootreg, index=8) #
boot.ci(Bootreg, type=“perc”, conf=c(0.90,0.95,0.99),index=1) # intercept boot.ci(Bootreg, type=“perc”, conf=c(0.90,0.95,0.99),index=2) # boot.ci(Bootreg, type=“perc”, conf=c(0.90,0.95,0.99),index=3) # boot.ci(Bootreg, type=“perc”, conf=c(0.90,0.95,0.99),index=4) # boot.ci(Bootreg, type=“perc”, conf=c(0.90,0.95,0.99), index=5) # boot.ci(Bootreg, type=“perc”, conf=c(0.90,0.95,0.99), index=6) # boot.ci(Bootreg, type=“perc”, conf=c(0.90,0.95,0.99), index=7) # boot.ci(Bootreg, type=“perc”, conf=c(0.90,0.95,0.99), index=8) # library(quantreg)

dev.off

summary(ms2_5)
## 
## Call:
## lm(formula = Item16 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48, data = sample2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.6007 -0.3932  0.0265  0.6465  1.7749 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -9.16964    1.97999  -4.631 7.06e-05 ***
## Age          0.41224    0.10288   4.007 0.000393 ***
## Gender2     -0.66994    0.40728  -1.645 0.110785    
## Item3        0.08671    0.13461   0.644 0.524542    
## Item7        0.55678    0.12776   4.358 0.000150 ***
## Item8       -0.11799    0.11103  -1.063 0.296678    
## Item48       0.59509    0.10141   5.868 2.29e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.147 on 29 degrees of freedom
## Multiple R-squared:      1,  Adjusted R-squared:      1 
## F-statistic: 1.215e+05 on 6 and 29 DF,  p-value: < 2.2e-16
summary(ms2_5) -> OLSreg2
coef2=OLSreg2$coefficients[,1]
error2=OLSreg2$coefficients[,2]  
ci2_1 <- list()
for (i in 1:length(coef2)){
ci2_1[[i]] <- coef2[i] + c(-1,1)*error2[i]*qnorm(0.995)}
ci2_1
## [[1]]
## [1] -14.269756  -4.069529
## 
## [[2]]
## [1] 0.1472319 0.6772517
## 
## [[3]]
## [1] -1.7190170  0.3791407
## 
## [[4]]
## [1] -0.2600303  0.4334523
## 
## [[5]]
## [1] 0.2276858 0.8858662
## 
## [[6]]
## [1] -0.4039822  0.1679977
## 
## [[7]]
## [1] 0.3338657 0.8563093
ci2_5 <- list()
for (i in 1:length(coef2)){
ci2_5[[i]] <- coef2[i] + c(-1,1)*error2[i]*qnorm(0.975)}
ci2_5
## [[1]]
## [1] -13.050349  -5.288935
## 
## [[2]]
## [1] 0.2105942 0.6138894
## 
## [[3]]
## [1] -1.4681885  0.1283123
## 
## [[4]]
## [1] -0.1771266  0.3505485
## 
## [[5]]
## [1] 0.3063693 0.8071827
## 
## [[6]]
## [1] -0.33560368  0.09961925
## 
## [[7]]
## [1] 0.3963222 0.7938527
ci2_10 <- list()
for (i in 1:length(coef2)){
ci2_10[[i]] <- coef2[i] + c(-1,1)*error2[i]*qnorm(0.95)}
ci2_10
## [[1]]
## [1] -12.42643  -5.91285
## 
## [[2]]
## [1] 0.2430138 0.5814698
## 
## [[3]]
## [1] -1.339851e+00 -2.528726e-05
## 
## [[4]]
## [1] -0.1347085  0.3081304
## 
## [[5]]
## [1] 0.3466281 0.7669240
## 
## [[6]]
## [1] -0.30061751  0.06463308
## 
## [[7]]
## [1] 0.4282784 0.7618965
# Bootstrap OLS regression
library(boot)
bs <- function(formula, data, indices) {
d <- data[indices,]  
   fit <- lm(formula, data=d)
   return(coef(fit)) 
 } 
Bootreg2 <-boot(data=sample2,statistic=bs,R=1000, formula=Item16 ~ Age + Gender + Item3 + Item7 + Item8 + Item48)
summary(Bootreg2)
## 
## Number of bootstrap replications R = 1000 
##    original   bootBias  bootSE   bootMed
## 1 -9.169642  2.5496622 3.70813 -7.170998
## 2  0.412242 -0.0845372 0.13561  0.339494
## 3 -0.669938  0.0077257 0.45872 -0.629844
## 4  0.086711 -0.0062995 0.20395  0.079166
## 5  0.556776 -0.0520218 0.16480  0.511920
## 6 -0.117992  0.0474462 0.16733 -0.079980
## 7  0.595087 -0.1117392 0.23335  0.555657
pdf(file="/Users/trekkatkins/Downloads/7585259/figure3.pdf")
plot(Bootreg2, index=1) # intercept 
plot(Bootreg2, index=2) # 
plot(Bootreg2, index=3) # 
plot(Bootreg2, index=4) # 
plot(Bootreg2, index=5) # 
plot(Bootreg2, index=6) # 
plot(Bootreg2, index=7) # 
boot.ci(Bootreg2, type="perc", conf=c(0.90,0.95,0.99), index=1) # intercept 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg2, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 1)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-11.684,   0.299 )   
## 95%   (-12.237,   1.342 )   
## 99%   (-13.593,   3.855 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg2, type="perc", conf=c(0.90,0.95,0.99), index=2) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg2, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 2)
## 
## Intervals : 
## Level     Percentile     
## 90%   ( 0.0931,  0.5312 )   
## 95%   ( 0.0564,  0.5672 )   
## 99%   (-0.0349,  0.6287 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg2, type="perc", conf=c(0.90,0.95,0.99), index=3) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg2, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 3)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-1.4552,  0.0204 )   
## 95%   (-1.6668,  0.1756 )   
## 99%   (-2.2482,  0.4214 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg2, type="perc", conf=c(0.90,0.95,0.99), index=4) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg2, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 4)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-0.2243,  0.3987 )   
## 95%   (-0.2893,  0.5053 )   
## 99%   (-0.4288,  0.7170 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg2, type="perc", conf=c(0.90,0.95,0.99), index=5) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg2, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 5)
## 
## Intervals : 
## Level     Percentile     
## 90%   ( 0.2199,  0.7589 )   
## 95%   ( 0.1623,  0.8116 )   
## 99%   (-0.0583,  0.9226 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg2, type="perc", conf=c(0.90,0.95,0.99), index=6) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg2, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 6)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-0.3212,  0.2217 )   
## 95%   (-0.3653,  0.2958 )   
## 99%   (-0.4732,  0.4563 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg2, type="perc", conf=c(0.90,0.95,0.99), index=7) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg2, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 7)
## 
## Intervals : 
## Level     Percentile     
## 90%   ( 0.0227,  0.7444 )   
## 95%   (-0.0931,  0.7898 )   
## 99%   (-0.2830,  0.8686 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
dev.off
## function (which = dev.cur()) 
## {
##     if (which == 1) 
##         stop("cannot shut down device 1 (the null device)")
##     .External(C_devoff, as.integer(which))
##     dev.cur()
## }
## <bytecode: 0x7f9720ffc478>
## <environment: namespace:grDevices>
# Quantile regression 
library(quantreg)
Qreg3 <- rq(Item16 ~ Age + Gender + Item3 + Item7 + Item8 + Item48, tau = .5, data=sample2)
summary(Qreg3, se="iid", bsmethod="xy")
## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique
## 
## Call: rq(formula = Item16 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48, tau = 0.5, data = sample2)
## 
## tau: [1] 0.5
## 
## Coefficients:
##             Value    Std. Error t value  Pr(>|t|)
## (Intercept) -4.81568  1.42306   -3.38404  0.00206
## Age          0.28679  0.07394    3.87847  0.00056
## Gender2     -0.38895  0.29272   -1.32876  0.19429
## Item3       -0.06352  0.09675   -0.65656  0.51664
## Item7        0.38113  0.09182    4.15067  0.00027
## Item8       -0.24932  0.07980   -3.12443  0.00402
## Item48       0.71833  0.07289    9.85532  0.00000
summary(Qreg3, se="iid", bsmethod="xy") -> Qreg4
## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique
coef3=Qreg4$coefficients[,1] 
error4=Qreg4$coefficients[,2]  
ci3_1 <- list()
for (i in 1:length(coef3)){
ci3_1[[i]] <- coef3[i] + c(-1,1)*error4[i]*qnorm(0.995)}
ci3_1
## [[1]]
## [1] -8.481226 -1.150127
## 
## [[2]]
## [1] 0.09632247 0.47725786
## 
## [[3]]
## [1] -1.1429466  0.3650397
## 
## [[4]]
## [1] -0.3127316  0.1856877
## 
## [[5]]
## [1] 0.1446082 0.6176552
## 
## [[6]]
## [1] -0.45487044 -0.04377749
## 
## [[7]]
## [1] 0.5305823 0.9060726
ci3_5 <- list()
for (i in 1:length(coef3)){
ci3_5[[i]] <- coef3[i] + c(-1,1)*error4[i]*qnorm(0.975)}
ci3_5
## [[1]]
## [1] -7.604815 -2.026538
## 
## [[2]]
## [1] 0.1418621 0.4317182
## 
## [[3]]
## [1] -0.9626714  0.1847644
## 
## [[4]]
## [1] -0.2531471  0.1261032
## 
## [[5]]
## [1] 0.2011596 0.5611038
## 
## [[6]]
## [1] -0.40572551 -0.09292242
## 
## [[7]]
## [1] 0.5754711 0.8611839
ci3_10 <- list()
for (i in 1:length(coef)){
ci3_10[[i]] <- coef3[i] + c(-1,1)*error4[i]*qnorm(0.95)}
ci3_10
## [[1]]
## [1] -7.156395 -2.474957
## 
## [[2]]
## [1] 0.1651627 0.4084176
## 
## [[3]]
## [1] -0.87043273  0.09252578
## 
## [[4]]
## [1] -0.22266037  0.09561647
## 
## [[5]]
## [1] 0.2300943 0.5321691
## 
## [[6]]
## [1] -0.3805803 -0.1180677
## 
## [[7]]
## [1] 0.5984386 0.8382164
## 
## [[8]]
## [1] NA NA
## 
## [[9]]
## [1] NA NA
## 
## [[10]]
## [1] NA NA
# Bootstrap Qunantile regression

library(quantreg)
bs <- function(formula, data, indices) {
d <- data[indices,]  
   fit <- rq(formula, tau=0.5, data=d)
   return(coef(fit)) 
 } 
library(quantreg)
library(boot)
Bootreg2 <-boot(data=sample2,statistic=bs,R=1000, formula=Item16 ~ Age + Gender + Item3 + Item7 + Item8 + Item48)
## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique

## Warning in rq.fit.br(x, y, tau = tau, ...): Solution may be nonunique
summary(Bootreg2)
## 
## Number of bootstrap replications R = 1000 
##    original   bootBias  bootSE   bootMed
## 1 -4.815676 -0.7048871 4.26996 -5.588947
## 2  0.286790  0.0184882 0.14335  0.289179
## 3 -0.388953  0.0024096 0.44246 -0.358754
## 4 -0.063522  0.0921699 0.22539 -0.025051
## 5  0.381132  0.1264780 0.27527  0.452632
## 6 -0.249324  0.0875476 0.16119 -0.166667
## 7  0.718327 -0.2250731 0.27752  0.577030
pdf(file="/Users/trekkatkins/Downloads/7585259/figure4.pdf")
plot(Bootreg2, index=1) # intercept 
plot(Bootreg2, index=2) # 
plot(Bootreg2, index=3) # 
plot(Bootreg2, index=4) # 
plot(Bootreg2, index=5) # 
plot(Bootreg2, index=6) # 
plot(Bootreg2, index=7) # 
boot.ci(Bootreg2, type="perc", conf=c(0.90,0.95,0.99),index=1) # intercept 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg2, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 1)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-11.886,   1.627 )   
## 95%   (-13.466,   3.111 )   
## 99%   (-15.741,   6.463 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg2, type="perc", conf=c(0.90,0.95,0.99),index=2) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg2, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 2)
## 
## Intervals : 
## Level     Percentile     
## 90%   ( 0.0932,  0.5537 )   
## 95%   ( 0.0345,  0.6165 )   
## 99%   (-0.1294,  0.7191 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg2, type="perc", conf=c(0.90,0.95,0.99),index=3) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg2, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 3)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-1.0323,  0.2812 )   
## 95%   (-1.2856,  0.4145 )   
## 99%   (-2.4281,  0.7827 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg2, type="perc", conf=c(0.90,0.95,0.99),index=4) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg2, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 4)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-0.2365,  0.4468 )   
## 95%   (-0.3389,  0.5823 )   
## 99%   (-0.5970,  0.9220 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg2, type="perc", conf=c(0.90,0.95,0.99),index=5) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg2, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 5)
## 
## Intervals : 
## Level     Percentile     
## 90%   ( 0.0591,  0.9589 )   
## 95%   ( 0.0212,  1.0137 )   
## 99%   (-0.0858,  1.0860 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg2, type="perc", conf=c(0.90,0.95,0.99),index=6) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg2, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 6)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-0.3706,  0.1391 )   
## 95%   (-0.4077,  0.2455 )   
## 99%   (-0.5550,  0.5806 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
boot.ci(Bootreg2, type="perc", conf=c(0.90,0.95,0.99),index=7) # 
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Bootreg2, conf = c(0.9, 0.95, 0.99), type = "perc", 
##     index = 7)
## 
## Intervals : 
## Level     Percentile     
## 90%   (-0.0536,  0.7736 )   
## 95%   (-0.2142,  0.8162 )   
## 99%   (-0.6705,  0.9330 )  
## Calculations and Intervals on Original Scale
## Some percentile intervals may be unstable
library(quantreg)

dev.off
## function (which = dev.cur()) 
## {
##     if (which == 1) 
##         stop("cannot shut down device 1 (the null device)")
##     .External(C_devoff, as.integer(which))
##     dev.cur()
## }
## <bytecode: 0x7f9720ffc478>
## <environment: namespace:grDevices>
library(lmSupport)  
## Registered S3 methods overwritten by 'lme4':
##   method                          from
##   cooks.distance.influence.merMod car 
##   influence.merMod                car 
##   dfbeta.influence.merMod         car 
##   dfbetas.influence.merMod        car
summary(m8)$adj.r.squared  # adjusted R^2
## [1] 0.2302801
summary(ms2_5)$adj.r.squared  # adjusted R^2
## [1] 0.999952
modelEffectSizes(m8)  # partial eta-squared
## lm(formula = Item16.1.75 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48 + Item49 + Item52 + Item54, data = sample)
## 
## Coefficients
##                  SSR df pEta-sqr dR-sqr
## (Intercept) 167.8519  1   0.1519     NA
## Age          51.7611  1   0.0523 0.0316
## Gender        0.0213  1   0.0000 0.0000
## Item3       128.8415  1   0.1208 0.0786
## Item7        16.8710  1   0.0177 0.0103
## Item8         1.4865  1   0.0016 0.0009
## Item48        1.8912  1   0.0020 0.0012
## Item49       11.3173  1   0.0119 0.0069
## Item52       73.4998  1   0.0727 0.0448
## Item54      238.4947  1   0.2028 0.1455
## 
## Sum of squared errors (SSE): 937.4
## Sum of squared total  (SST): 1639.5
modelEffectSizes(ms2_5)  # partial eta-squared
## lm(formula = Item16 ~ Age + Gender + Item3 + Item7 + Item8 + 
##     Item48, data = sample2)
## 
## Coefficients
##                 SSR df pEta-sqr dR-sqr
## (Intercept) 28.2226  1   0.4251     NA
## Age         21.1267  1   0.3563      0
## Gender       3.5604  1   0.0853      0
## Item3        0.5460  1   0.0141      0
## Item7       24.9909  1   0.3957      0
## Item8        1.4861  1   0.0375      0
## Item48      45.3100  1   0.5428      0
## 
## Sum of squared errors (SSE): 38.2
## Sum of squared total  (SST): 959172.3